SAT Mathematics : Inequalities & Absolute Value

Study concepts, example questions & explanations for SAT Mathematics

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Example Questions

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Example Question #9 : Understanding Inequalities

Which of the following expresses the complete set of values for  that satisfy the inequality above?

Possible Answers:

Correct answer:

Explanation:

In order to tackle this question, we'll want to keep in mind that inequalities follow all the same rules and operations as equations - with one important exception. When we multiply or divide by a negative, we have to flip the inequality sign, as we are basically "flipping" the relationship over 0 on the number line. (A number that is larger when positive becomes "more negative," and thus smaller when negative, and vice versa).  

In this case, we start by getting rid of our denominator by multiplying both sides of our inequality by 4

 

we can then subtract two from both sides to get to

and divide both sides by -3, (keeping in mind that we need to flip the sign when we do so!)

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