Which of the following is the solution to the equation (A)

In Exercises 1 and 2, simplify the expression by combining like terms. 2x + 5x + 7 + y - 3x + 4y + 2

In Exercises 1 and 2, simplify the expression by combining like terms. 4 + 2x - 3z + 5y - x + 2y - z - 2

In Exercises 3 and 4, use the distributive property to expand the products. Simplify the resulting expression by combining like terms. 3(2x - y) + 4(y - x) + x + y

In Exercises 3 and 4, use the distributive property to expand the products. Simplify the resulting expression by combining like terms. 5(2x + y - 1) + 4(y - 3x + 2) + 1

In Exercises 5–10, use the LCD to combine the fractions. Simplify the resulting fraction. \(\frac{2}{y}+\frac{3}{y}\)

In Exercises 5–10, use the LCD to combine the fractions. Simplify the resulting fraction. \(\frac{1}{y-1}+\frac{3}{y-2}\)

In Exercises 5–10, use the LCD to combine the fractions. Simplify the resulting fraction. \(2+\frac{1}{x}\)

In Exercises 5–10, use the LCD to combine the fractions. Simplify the resulting fraction. \(\frac{1}{x}+\frac{1}{y}-x\)

In Exercises 5–10, use the LCD to combine the fractions. Simplify the resulting fraction. \(\frac{x+4}{2}+\frac{3 x-1}{5}\)

In Exercises 5–10, use the LCD to combine the fractions. Simplify the resulting fraction. \(\frac{x}{3}+\frac{x}{4}\)

In Exercises 1–4, find which values of x are solutions of the equation. \(2x^2 + 5x = 3\) (a) x = -3 (b) \(x = -\frac{1}{2}\) (c) \(x = \frac{1}{2}\)

In Exercises 1–4, find which values of x are solutions of the equation. \(\frac{x}{2} + \frac{1}{6} = \frac{x}{3}\) (a) x = -1 (b) x = 0 (c) x = 1

In Exercises 1–4, find which values of x are solutions of the equation. \(\sqrt{1-x^2} + 2 = 3\) (a) x = -2 (b) x = 0 (c) x = 2

In Exercises 1–4, find which values of x are solutions of the equation. \((x - 2)^{1/3} = 2\) (a) x = -6 (b) x = 8 (c) x = 10

In Exercises 5–10, determine whether the equation is linear in x. 5 - 3x = 0

In Exercises 5–10, determine whether the equation is linear in x. 5 = 10/2

In Exercises 5–10, determine whether the equation is linear in x. x + 3 = x - 5

In Exercises 5–10, determine whether the equation is linear in x. \(x - 3 = x^2\)

In Exercises 5–10, determine whether the equation is linear in x. \(2\sqrt{x} + 5 = 10\)

In Exercises 5–10, determine whether the equation is linear in x. \(x + \frac{1}{x} = 1\)

In Exercises 11–24, solve the equation without using a calculator. 3x = 24

In Exercises 11–24, solve the equation without using a calculator. 4x = -16

In Exercises 11–24, solve the equation without using a calculator. 3t - 4 = 8

In Exercises 11–24, solve the equation without using a calculator. 2t - 9 = 3

In Exercises 11–24, solve the equation without using a calculator. 2x - 3 = 4x - 5

In Exercises 11–24, solve the equation without using a calculator. 4 - 2x = 3x - 6

In Exercises 11–24, solve the equation without using a calculator. 4 - 3y = 2(y + 4)

In Exercises 11–24, solve the equation without using a calculator. 4(y - 2) = 5y

In Exercises 11–24, solve the equation without using a calculator. \(\frac{1}{2}x = \frac{7}{8}\)

In Exercises 11–24, solve the equation without using a calculator. \(\frac{2}{3}x = \frac{4}{5}\)

In Exercises 11–24, solve the equation without using a calculator. \(\frac{1}{2}x + \frac{1}{3} = 1\)

In Exercises 11–24, solve the equation without using a calculator. \(\frac{1}{3}x + \frac{1}{4} = 1\)

In Exercises 11–24, solve the equation without using a calculator. 2(3 - 4z) - 5(2z + 3) = z - 17

In Exercises 11–24, solve the equation without using a calculator. 3(5z - 3) - 4(2z + 1) = 5z - 2

In Exercises 25–28, solve the equation. Support your answer with a calculator. \(\frac{2 x-3}{4}+5=3 x\)

In Exercises 25–28, solve the equation. Support your answer with a calculator. \(2 x-4=\frac{4 x-5}{3}\)

In Exercises 25–28, solve the equation. Support your answer with a calculator. \(\frac{t+5}{8}-\frac{t-2}{2}=\frac{1}{3}\)

In Exercises 25–28, solve the equation. Support your answer with a calculator. \(\frac{t-1}{3}+\frac{t+5}{4}=\frac{1}{2}\)

Writing to Learn Write a statement about solutions of equations suggested by the computations in the figure.

Writing to Learn Write a statement about solutions of equations suggested by the computations in the figure.

In Exercises 31–34, find which values of x are solutions of the inequality. 2x - 3 < 7 (a) x = 0 (b) x = 5 (c) x = 6

In Exercises 31–34, find which values of x are solutions of the inequality. \(3x - 4\ \geq\ 5\) (a) x = 0 (b) x = 3 (c) x = 4

In Exercises 31–34, find which values of x are solutions of the inequality. \(-1 < 4x - 1\ \leq\ 11\) (a) x = 0 (b) x = 2 (c) x = 3

In Exercises 31–34, find which values of x are solutions of the inequality. \(-3\ \leq\ 1 - 2x\ \leq\ 3\) (a) x = -1 (b) x = 0 (c) x = 2

In Exercises 35–42, solve the inequality, and draw a number line graph of the solution set. x - 4 < 2

In Exercises 35–42, solve the inequality, and draw a number line graph of the solution set. x + 3 > 5

In Exercises 35–42, solve the inequality, and draw a number line graph of the solution set. \(2x - 1\ \leq\ 4x + 3\)

In Exercises 35–42, solve the inequality, and draw a number line graph of the solution set. \(3x - 1\ \geq\ 6x + 8\)

In Exercises 35–42, solve the inequality, and draw a number line graph of the solution set. \(2\ \leq\ x + 6 < 9\)

In Exercises 35–42, solve the inequality, and draw a number line graph of the solution set. \(-1\ \leq\ 3x - 2 < 7\)

In Exercises 35–42, solve the inequality, and draw a number line graph of the solution set. \(2(5 - 3x) + 3(2x - 1)\ \leq\ 2x + 1\)

In Exercises 35–42, solve the inequality, and draw a number line graph of the solution set. 4(1 - x) + 5(1 + x) > 3x - 1

In Exercises 43–54, solve the inequality. \(\frac{5 x+7}{4} \leq-3\)

In Exercises 43–54, solve the inequality. \(\frac{3 x-2}{5}>-1\)

In Exercises 43–54, solve the inequality. \(4 \geq \frac{2 y-5}{3} \geq-2\)

In Exercises 43–54, solve the inequality. \(1>\frac{3 y-1}{4}>-1\)

In Exercises 43–54, solve the inequality. \(0 \leq 2 z+5<8\)

In Exercises 43–54, solve the inequality. \(-6\ <\ 5t - 1\ < 0\)

In Exercises 43–54, solve the inequality. \(\frac{x-5}{4}+\frac{3-2 x}{3}<-2\)

In Exercises 43–54, solve the inequality. \(\frac{3-x}{2}+\frac{5 x-2}{3}<-1\)

In Exercises 43–54, solve the inequality. \(\frac{2 y-3}{2}+\frac{3 y-1}{5}<y-1\)

In Exercises 43–54, solve the inequality. \(\frac{3-4 y}{6}-\frac{2 y-3}{8} \geq 2-y\)

In Exercises 43–54, solve the inequality. \(\frac{1}{2}(x-4)-2 x \leq 5(3-x)\)

In Exercises 43–54, solve the inequality. \(\frac{1}{2}(x+3)+2(x-4)<\frac{1}{3}(x-3)\)

In Exercises 55–58, find the solutions of the equation or inequality displayed in Figure P.20. \(x^2 - 2x\ <\ 0\) FIGURE P.20 The second column gives values of \(y_1 = x^2 - 2x\) for x = 0, 1, 2, 3, 4, 5, and 6.

In Exercises 55–58, find the solutions of the equation or inequality displayed in Figure P.20. \(x^2 - 2x = 0\) FIGURE P.20 The second column gives values of \(y_1 = x^2 - 2x\) for x = 0, 1, 2, 3, 4, 5, and 6.

In Exercises 55–58, find the solutions of the equation or inequality displayed in Figure P.20. \(x^2 - 2x\ >\ 0\) FIGURE P.20 The second column gives values of \(y_1 = x^2 - 2x\) for x = 0, 1, 2, 3, 4, 5, and 6.

In Exercises 55–58, find the solutions of the equation or inequality displayed in Figure P.20. \(x^2 - 2x\ \leq\ 0\) FIGURE P.20 The second column gives values of \(y_1 = x^2 - 2x\) for x = 0, 1, 2, 3, 4, 5, and 6.

Writing to Learn Explain how the second equation was obtained from the first. x - 3 = 2x + 3, 2x - 6 = 4x + 6

Writing to Learn Explain how the second equation was obtained from the first. \(2 x-1=2 x-4, \quad x-\frac{1}{2}=x-2\)

Group Activity Determine whether the two equations are equivalent. (a) 3x = 6x + 9, x = 2x + 9 (b) 6x + 2 = 4x + 10, 3x + 1 = 2x + 5

Group Activity Determine whether the two equations are equivalent. (a) 3x + 2 = 5x - 7, -2x + 2 = -7 (b) 2x + 5 = x - 7, 2x = x - 7

True or False -6 > -2. Justify your answer.

True or False \(2\ \leq\ \frac{6}{3}\). Justify your answer.

In Exercises 65–68, you may use a graphing calculator to solve these problems. Multiple Choice: Which of the following equations is equivalent to the equation 3x + 5 = 2x + 1? (A) 3x = 2x (B) 3x = 2x + 4 (C) \(\frac{3}{2}x + \frac{5}{2} = x + 1\) (D) 3x + 6 = 2x (E) 3x = 2x - 4

In Exercises 65–68, you may use a graphing calculator to solve these problems. Multiple Choice Which of the following inequalities is equivalent to the inequality -3x < 6? (A) 3x < -6 (B) x < 10 (C) x > -2 (D) x > 2 (E) x > 3

In Exercises 65–68, you may use a graphing calculator to solve these problems. Multiple Choice Which of the following is the solution to the equation x(x + 1) = 0? (A) x = 0 or x = -1 (B) x = 0 or x = 1 (C) Only x = -1 (D) Only x = 0 (E) Only x = 1

In Exercises 65–68, you may use a graphing calculator to solve these problems. Multiple Choice Which of the following represents an equation equivalent to the equation \(\frac{2 x}{3}+\frac{1}{2}=\frac{x}{4}-\frac{1}{3}\) that is cleared of fractions? (A) 2x + 1 = x - 1 (B) 8x + 6x = 3x - 4 (C) \(4x + 3 = \frac{3}{2}x - 2\) (D) 4x + 3 = 3x - 4 (E) 4x + 6 = 3x - 4

Testing Inequalities on a Calculator (a) The calculator we use indicates that the statement 2 < 3 is true by returning the value 1 (for true) when 2 < 3 is entered. Try it with your calculator. (b) The calculator we use indicates that the statement 2 < 1 is false by returning the value 0 (for false) when 2 < 1 is entered. Try it with your calculator. (c) Use your calculator to test which of these two numbers is larger: 799/800, 800/801. (d) Use your calculator to test which of these two numbers is larger: -102/111, -103/102. (e) If your calculator returns 0 when you enter 2x + 1 < 4, what can you conclude about the value stored in x?

Perimeter of a Rectangle The formula for the perimeter P of a rectangle is P = 2(L + W). Solve this equation for W.

Area of a Trapezoid The formula for the area A of a trapezoid is \(A = \frac{1}{2}h (b_1 + b_2)\). Solve this equation for \(b_1\).

Volume of a Sphere The formula for the volume V of a sphere is \(V = \frac{4}{3} \pi r^3\). Solve this equation for r.

Celsius and Fahrenheit The formula for Celsius temperature in terms of Fahrenheit temperature is \(C = \frac{5}{9}(F - 32)\). Solve the equation for F.