GRE Subject Test: Math : Absolute Value Inequalities

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

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Example Question #11 : Absolute Value Inequalities

Possible Answers:

 or 

 and

 and

There is no solution.

Correct answer:

 or 

Explanation:

At this point, you've isolated the absolute value and can solve this problems for both cases,  and .  Beginning with the first case:

 

 

Then for the second case:

Example Question #12 : Absolute Value Inequalities

Possible Answers:

or

or

 and 

Correct answer:

 and 

Explanation:

Since the absolute value with x in it is alone on one side of the inequality, you set the expression inside the absolute value equal to both the positive and negative value of the other side, 11 and -11 in this case. For the negative value -11, you must also flip the inequality from less than to a greater than. You should have two inequalities looking like this.

and

Add 5 to both sides in each inequality.

and

Divide by -4 to both sides of the inequality. Remember, dividing by a negative will flip both inequality symbols and you should have this.

and

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