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# Review Sheet for MATH 1310 at UH

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This 6 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 20 views.

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Date Created: 02/06/15

1310 Section 26 Linear Inequalities Linear 7 means that the variable is to the first power Inequality 7 means that the comparative symbol is one of the following S lt 2 gt So we re comparing and there s a boundary involved For example ifI say X gt 5 I mean for you to think of numbers strictly bigger than 50 555 is an example of this type of X I can use interval notation to summarize all these X s 5 Or I can use a graph with a numberline featuring a hollow dot at 5 Notice this can become an X aXis if I put in the y aXis 4 o gt 5 Inequalities have the feature that you may add and subtract a number to both sides and you will get an equivalent inequality You may multiply and divide by a positive number and you will get an equivalent inequality If you multiply or divide by a negative number you induce a ip about the centerpoint zero and we symbolize this by ipping the inequality symbol So Solve 5X 32 8 Subtract 3 from both sides Now the claim is that negative 5 times X is greater than positive 5 What kind of numbers are our X s if the product of X and 5 is a positive Indeed the X s are negatives Divide both sides by 5 What happens if we forget to ip the inequality Put your answer in interval notation and sketch a graph of your answer How about 6X 3 lt 9X 15 Now we can have compound inequalities too You must read these carefully Here is a simple one the X s I care about are between and including 3 and 5 33 XS 5 Saying 35 and both mean the same X s 3 5 Now it s possible to get compound inequality problems too Let s solve this one NlH only 3lt 5 xlt 12 Now compound inequalities can be outies as well as innies Let s look at the inequality expression for How would you write the manglish for this picture using inequality symbols The key word is or How would you write this in interval notation Or is written U a union of two rays Let s reView CTS X2 26X 7 0 Now let s move into Absolute Value Section 28 Most everybody can tell me what the absolute value of 3 is But 7 I want you to start thinking of absolute value as a distance Indeed as a distance from zero If I tell you to read out loud and draw a picture of the following equation le 3 I ll be expecting to hear The distance from X to zero is 3 and I ll expect a picture that looks like this 439 quotquotquotquotquotquotquotquotquotquotquotquotquotquotquot quotC quotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquotquot quotC quotquotquotquotquotquotquotquotquotquot quotF 3 3 There are two places on the number line that are 3 away from zero The answer is X 3 or X 3 When you get absolute value equations then the problem is then two problems the negative problem and the positive problem Lookat l3x 5 11 From order of operations you know that you need to remove the absolute value problem delimiters before continuing We ll do that by reading the problem and translating our words to set of problems This says The distance from 3X 5 to zero is 11 Well now there are two places that are 11 away from zero on the number line So we ll solve both problems 4 o o gt 3X 5 11 0 3X 511 Let s do another 3 X 15 And another 2 2x 3 12

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