SAT Math : Inequalities

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #1 : Inequalities

What is the solution set of the inequality \dpi{100} \small 3x+8<35 ?

Possible Answers:

\dpi{100} \small x>9

\dpi{100} \small x<9

\dpi{100} \small x>27

\dpi{100} \small x<27

\dpi{100} \small x<35

Correct answer:

\dpi{100} \small x<9

Explanation:

We simplify this inequality similarly to how we would simplify an equation

\dpi{100} \small 3x+8-8<35-8

\dpi{100} \small \frac{3x}{3}<\frac{27}{3}

Thus \dpi{100} \small x<9

Example Question #6 : Inequalities

What is a solution set of the inequality ?

Possible Answers:

Correct answer:

Explanation:

In order to find the solution set, we solve  as we would an equation:

Therefore, the solution set is any value of .

Example Question #1 : How To Find The Solution To An Inequality With Division

Which of the following could be a value of , given the following inequality?

Possible Answers:

Correct answer:

Explanation:

The inequality that is presented in the problem is:

Start by moving your variables to one side of the inequality and all other numbers to the other side:

Divide both sides of the equation by . Remember to flip the direction of the inequality's sign since you are dividing by a negative number!

Reduce:

The only answer choice with a value greater than  is .

Example Question #42 : Inequalities

If  and , which of the following gives the set of possible values of ?

Possible Answers:

Correct answer:

Explanation:

To get the lowest value, you need the lowest numerator and the highest denominator.  That would be  or reduced to be .  For the highest value, you need the highest numerator and the lowest denominator.  That would be  or .

Example Question #43 : Inequalities

Give the solution set of this inequality:

Possible Answers:

The inequality has no solution.

Correct answer:

Explanation:

The inequality  can be rewritten as the three-part inequality

Isolate the  in the middle expression by performing the same operations in all three expressions. Subtract 32 from each expression:

Divide each expression by , switching the direction of the inequality symbols:

This can be rewritten in interval notation as .

Example Question #44 : Inequalities

Give the solution set of this inequality:

Possible Answers:

The inequality has no solution.

Correct answer:

The inequality has no solution.

Explanation:

In an absolute value inequality, the absolute value expression must be isolated first, as follows:

Adding 12 to both sides:

Multiplying both sides by , and switching the inequality symbol due to multiplication by a negative number:

We do not need to go further. An absolute value expression must always be greater than or equal to 0; it is impossible for the expression  to be less than any negative number. The inequality has no solution.

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