Solved: ?Solve Inequalities using the Division and Multiplication Properties of

Graph on the number line: (a) \(x \leq-1\) (b) x > 2 (c) x < 3 Equation Transcription: Text Transcription: x leq -1

Graph on the number line: (a) x > ?2 (b) x < ?3 (c) \(x \geq-1\) Equation Transcription: Text Transcription: x geq -1

Graph on the number line and write in interval notation: (a) x > 2 (b) \(x \leq-1.5\) (c) \(x \geq \frac{3}{4}\) Equation Transcription: Text Transcription: x leq -1.5 x geq 3/4

Graph on the number line and write in interval notation: (a) \(x \leq-4\) (b) \(x \geq 0.5\) (c) \(x < -\frac{2}{3}\) Equation Transcription: Text Transcription: x leq -4 x geq 0.5 x < -2/3

Solve the inequality, graph the solution on the number line, and write the solution in interval notation. \(p-\frac{3}{4} \geq \frac{1}{6}\) Equation Transcription: Text Transcription: p-3/4 geq 1/6

Solve the inequality, graph the solution on the number line, and write the solution in interval notation. \(r-\frac{1}{3} \leq \frac{7}{12}\) Equation Transcription: Text Transcription: r-1/3 leq 7/12

Solve the inequality, graph the solution on the number line, and write the solution in interval notation. \((8, \infty)\) Equation Transcription: Text Transcription: (8, infinity)

Solve the inequality, graph the solution on the number line, and write the solution in interval notation. \(12 d \leq 60\) Equation Transcription: Text Transcription: 12d leq 60

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. ?8q < 32

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(-7 r \leq-70\) Equation Transcription: Text Transcription: -7r leq -70

Solve the inequality, graph the solution on the number line, and write the solution in interval notation. \(24 \leq \frac{3}{8} m\) Equation Transcription: Text Transcription: 24 leq 3/8m

Solve the inequality, graph the solution on the number line, and write the solution in interval notation. \(-24 < \frac{4}{3} n\) Equation Transcription: Text Transcription: -24<4/3n

Solve the inequality, graph the solution on the number line, and write the solution in interval notation. \(\frac{k}{-12} \leq 15\) Equation Transcription: Text Transcription: k/12 leq 15

Solve the inequality, graph the solution on the number line, and write the solution in interval notation. \(\frac{u}{-4} \geq -16\) Equation Transcription: Text Transcription: u/-4 geq -16

Solve the inequality \(3 q \geq 7 q-23\), graph the solution on the number line, and write the solution in interval notation. Equation Transcription: Text Transcription: 3q geq 7q?23

Solve the inequality 6x < 10x + 19, graph the solution on the number line, and write the solution in interval notation.

Solve the inequality 9y + 2(y + 6) > 5y ? 24, graph the solution on the number line, and write the solution in interval notation.

Solve the inequality 6u + 8(u ? 1) > 10u + 32, graph the solution on the number line, and write the solution in interval notation.

Solve the inequality 4b ? 3(3 ? b) > 5(b ? 6) + 2b, graph the solution on the number line, and write the solution in interval notation.

Solve the inequality 9h ? 7(2 ? h) < 8(h + 11) + 8h, graph the solution on the number line, and write the solution in interval notation.

Solve the inequality \(\frac{1}{4} x-\frac{1}{12} x>\frac{1}{6} x+\frac{7}{8}\),graph the solution on the number line, and write the solution in interval notation. Equation Transcription: Text Transcription: 1/4x-1/12x>1/6x+7/8

Solve the inequality \(\frac{2}{5} z-\frac{1}{3} z<\frac{1}{15} z-\frac{3}{5}\),graph the solution on the number line, and write the solution in interval notation. Equation Transcription: Text Transcription: 2/5z-1/3z<1/15z-3/5

Translate and solve. Then write the solution in interval notation and graph on the number line. Twenty times y is at most 100

Translate and solve. Then write the solution in interval notation and graph on the number line. Nine times z is no less than 135

Translate and solve. Then write the solution in interval notation and graph on the number line. Nineteen less than p is no less than 47

Translate and solve. Then write the solution in interval notation and graph on the number line. Four more than a is at most 15.

Graph Inequalities on the Number Line In the following exercises, graph each inequality on the number line. (a) \(x \leq-2\) (b) x > -1 (c) x < 0 Equation Transcription: Text Transcription: x leq -2

Graph Inequalities on the Number Line In the following exercises, graph each inequality on the number line. (a) x > 1 (b) x < -2 (c) \(x \geq-3\) Equation Transcription: Text Transcription: x geq -3

Graph Inequalities on the Number Line In the following exercises, graph each inequality on the number line. (a) \(x \geq-1\) (b) x < 4 (c) \(x \leq-2\) Equation Transcription: Text Transcription: x geq -1 x leq -2

Graph Inequalities on the Number Line In the following exercises, graph each inequality on the number line. (a) \(x \leq 0\) (b) x > -4 (c) \(x \geq-1\) Equation Transcription: Text Transcription: x leq 0 x geq -1

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. 8x > 72

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. 6y < 48

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(7 r \leq 56\) Equation Transcription: Text Transcription: 7r leq 56

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(9 s \geq 81\) Equation Transcription: Text Transcription: 9s geq 81

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(-5 u \geq 65\) Equation Transcription: Text Transcription: -5u geq 65

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(-8 v \leq 96\) Equation Transcription: Text Transcription: -8v leq 96

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. ?9c < 126

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. ?7d > 105

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(20>\frac{2}{5} h\) Equation Transcription: Text Transcription: 20>2/5h

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(40<\frac{5}{8} k\) Equation Transcription: Text Transcription: 40<5/8k

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(\frac{7}{6} j \geq 42\) Equation Transcription: Text Transcription: 7/6j geq 42

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(\frac{9}{4} g \leq 36\) Equation Transcription: Text Transcription: 9/4g leq 36

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(\frac{a}{-3} \leq 9\) Equation Transcription: Text Transcription: a-3 leq 9

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(\frac{b}{-10} \geq 30\) Equation Transcription: Text Transcription: b/-10 geq 30

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(-25<\frac{p}{-5}\) Equation Transcription: Text Transcription: -25<p/-5

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(-18>\frac{q}{-6}\) Equation Transcription: Text Transcription: -18>q/-6

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(9 t \geq-27\) Equation Transcription: Text Transcription: 9t geq -27

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. 7s < -28

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(\frac{2}{3} y>-36\) Equation Transcription: Text Transcription: 2/3y>-36

Solve Inequalities using the Division and Multiplication Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(\frac{3}{5} x \leq-45\) Equation Transcription: Text Transcription: 3/5x-45

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(4 v \geq 9 v-40\) Equation Transcription: Text Transcription: 4v geq 9v-40

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(5 u \leq 8 u-21\) Equation Transcription: Text Transcription: 5u leq 8u-21

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. 13q < 7q ? 29

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. 9p > 14p ? 18

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. 12x + 3(x + 7) > 10x ? 24

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. 9y + 5(y + 3) < 4y ? 35

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(6 h-4(h-1) \leq 7 h-11\) Equation Transcription: Text Transcription: 6h-4(h-1) leq 7h-11

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(4 k-(k-2) \geq 7 k-26\) Equation Transcription: Text Transcription: 4k-(k-2) geq 7k-26

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(8 m-2(14-m) \geq 7(m-4)+3 m\) Equation Transcription: Text Transcription: 8m-2(14-m) geq 7(m-4)+3m

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(6 n-12(3-n) \leq 9(n-4)+9 n\) Equation Transcription: Text Transcription: 6n-12(3-n) leq 9(n-4)+9n

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(\frac{3}{4} b-\frac{1}{3} b<\frac{5}{12} b-\frac{1}{2}\) Equation Transcription: Text Transcription: 3/4b-1/3b<5/12b-1/2

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(9 u+5(2 u-5) \geq 12(u-1)+7 u\) Equation Transcription: Text Transcription: 9u+5(2u-5) geq 12(u-1)+7u

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(\frac{2}{3} g-\frac{1}{2}(g-14) \leq \frac{1}{6}(g+42)\) Equation Transcription: Text Transcription: 2/3g-1/2(g-14) leq 1/6(g+42)

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(\frac{5}{6} u-\frac{1}{4} a>\frac{7}{12} a+\frac{2}{3}\) Equation Transcription: Text Transcription: 5/6u-1/4a>7/12a+2/3

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(\frac{4}{5} h-\frac{2}{3}(h-9) \geq \frac{1}{15}(2 h+90)\) Equation Transcription: Text Transcription: 4/5h-2/3(h-9) geq 1/15(2h+90)

Solve Inequalities That Require Simplification In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(12 v+3(4 v-1) \leq 19(v-2)+5 v\) Equation Transcription: Text Transcription: 12v+3(4v-1) leq 19(v-2)+5v

Mixed practice In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(15 k \leq-40\) Equation Transcription: Text Transcription: 15k leq -40

Mixed practice In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(35 k \geq-77\) Equation Transcription: Text Transcription: 35k geq -77

Mixed practice In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(23 p-2(6-5 p)>3(11 p-4)\) Equation Transcription: Text Transcription: 23p-2(6-5p)>3(11p-4)

Mixed practice In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(18 q-4(10-3 q)<5(6 q-8)\) Equation Transcription: Text Transcription: 18q-4(10-3q)<5(6q-8)

Mixed practice In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(-\frac{9}{4} x \geq-\frac{5}{12}\) Equation Transcription: Text Transcription: -9/4x geq -5/12

Mixed practice In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(-\frac{21}{8} y \leq-\frac{15}{28}\) Equation Transcription: Text Transcription: -21/8y leq -15/28

Mixed practice In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(c+34<-99\) Equation Transcription: Text Transcription: c+34<-99

Mixed practice In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(d+29>-61\) Equation Transcription: Text Transcription: d+29>-61

Mixed practice In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(\frac{m}{18} \geq-4\) Equation Transcription: Text Transcription: m/18 geq -4

Mixed practice In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(\frac{n}{13} \leq-6\) Equation Transcription: Text Transcription: n/13 leq -6

Translate to an Inequality and Solve In the following exercises, translate and solve .Then write the solution in interval notation and graph on the number line. Fourteen times d is greater than 56.

Translate to an Inequality and Solve In the following exercises, translate and solve .Then write the solution in interval notation and graph on the number line. Ninety times c is less than 450.

Translate to an Inequality and Solve In the following exercises, translate and solve .Then write the solution in interval notation and graph on the number line. Eight times z is smaller than ?40.

Translate to an Inequality and Solve In the following exercises, translate and solve .Then write the solution in interval notation and graph on the number line. Ten times y is at most ?110.

Translate to an Inequality and Solve In the following exercises, translate and solve .Then write the solution in interval notation and graph on the number line. Three more than his no less than 25.

Translate to an Inequality and Solve In the following exercises, translate and solve .Then write the solution in interval notation and graph on the number line. Six more than k exceeds 25.

Translate to an Inequality and Solve In the following exercises, translate and solve .Then write the solution in interval notation and graph on the number line. Ten less than w is at least 39.

Translate to an Inequality and Solve In the following exercises, translate and solve .Then write the solution in interval notation and graph on the number line. Twelve less than x is no less than 21.

Translate to an Inequality and Solve In the following exercises, translate and solve .Then write the solution in interval notation and graph on the number line. Negative five times r is no more than 95.

Translate to an Inequality and Solve In the following exercises, translate and solve .Then write the solution in interval notation and graph on the number line. Negative two times s is lower than 56.

Translate to an Inequality and Solve In the following exercises, translate and solve .Then write the solution in interval notation and graph on the number line. Nineteen less than b is at most ?22.

Translate to an Inequality and Solve In the following exercises, translate and solve .Then write the solution in interval notation and graph on the number line. Fifteen less than a is at least ?7.

Everyday Math Safety A child’s height, h, must be at least 57 inches for the child to safely ride in the front seat of a car. Write this as an inequality.

Everyday Math Fighter pilots The maximum height, h, of a fighter pilot is 77 inches. Write this as an inequality.

Everyday Math Elevators The total weight, w, of an elevator’s passengers can be no more than 1,200 pounds. Write this as an inequality.

Everyday Math Shopping The number of items, n, a shopper can have in the express check-out lane is at most 8. Write this as an inequality.

Writing Exercises Give an example from your life using the phrase ‘at least’.

Writing Exercises Give an example from your life using the phrase ‘at most’.

Writing Exercises Explain why it is necessary to reverse the inequality when solving ?5x > 10.

Writing Exercises Explain why it is necessary to reverse the inequality when solving \(\frac{n}{-3}<12\). Equation Transcription: Text Transcription: n/-3<12

Graph Inequalities on the Number Line In the following exercises, graph each inequality on the number line and write in interval notation. (a) x < -2 (b) \(x \geq-3.5\) (c) \(x \leq \frac{2}{3}\) Text Transcription: x geq -3.5 x leq 2/3

Graph Inequalities on the Number Line In the following exercises, graph each inequality on the number line and write in interval notation. (a) x > 3 (b) \(x \leq-0.5\) (c) \(x \geq \frac{1}{3}\) Text Transcription: x leq -0.5 x geq 1/3

Graph Inequalities on the Number Line In the following exercises, graph each inequality on the number line and write in interval notation. (a) \(x \geq-4\) (b) x < 2.5 (c) \(x>-\frac{3}{2}\) Text Transcription: x geq -4 x > -3/2

Graph Inequalities on the Number Line In the following exercises, graph each inequality on the number line and write in interval notation. (a) \(x \leq 5\) (b) \(x \geq-1.5\) (c) \(x<-\frac{7}{3}\) Text Transcription: x leq 5 x geq-1.5 x < -7/3

Solve Inequalities using the Subtraction and Addition Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. n - 11 < 35

Solve Inequalities using the Subtraction and Addition Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(m-45 \leq 62\) Text Transcription: m-45 leq 62

Solve Inequalities using the Subtraction and Addition Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. u + 25 > 21

Solve Inequalities using the Subtraction and Addition Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. v + 12 > 3

Solve Inequalities using the Subtraction and Addition Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(a+\frac{3}{4} \geq \frac{7}{10}\) Text Transcription: a+3/4 geq 7/10

Solve Inequalities using the Subtraction and Addition Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(b+\frac{7}{8} \geq \frac{1}{6}\) Text Transcription: b+7/8 geq 1/6

Solve Inequalities using the Subtraction and Addition Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(f-\frac{13}{20}<-\frac{5}{12}\) Text Transcription: f-13/20 < -5/12

Solve Inequalities using the Subtraction and Addition Properties of Inequality In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(g-\frac{11}{12}<-\frac{5}{18}\) Text Transcription: g-11/12 < - 5/18