Inequalities — ISEE Upper practice questions

On the ISEE Upper Mathematics Achievement section, Inequalities asks students to solve linear and absolute-value inequalities, rewrite an inequality in an equivalent form, and describe every value that satisfies a given statement. A typical item presents a single-variable inequality and asks for the solution set, an equivalent inequality, or the inequality that describes all values of the unknown. Answer choices are usually other inequalities written in inequality notation. A common trap is forgetting to reverse the sign when multiplying or dividing by a negative number; another is mishandling the two-sided meaning of an absolute-value comparison.

Section: Mathematics Achievement 47 questions on the paper
85 practice questions in the app

Sample questions

Question 1

What is the solution set of $|3x-5|<16$ ?

A $x < -\dfrac{11}{3}$ or $x > 7$
B $-7 < x < \dfrac{11}{3}$
C $-\dfrac{11}{3} < x < 7$
D $x < 7$

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Answer: C — $-\dfrac{11}{3} < x < 7$

$|3x-5|<16$ is equivalent to $-16<3x-5<16$ . Adding 5 to all three parts gives $-11<3x<21$ . Dividing by 3 gives $-\dfrac{11}{3}<x<7$ .

Question 2

Which inequality is equivalent to $-2<3x+4\le13$ ?

A $-2<x\le3$
B $-2\le x<3$
C $x\le-2$ or $x>3$
D $2<x\le17$

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Answer: A — $-2<x\le3$

Subtracting 4 gives $-6<3x\le9$ . Dividing by 3 gives $-2<x\le3$ .

Question 3

If $-4y + 7 > 27$ , which inequality describes all values of $y$ ?

A $y > -5$
B $y < -5$
C $y > 5$
D $y < 5$

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Answer: B — $y < -5$

Subtract 7 from both sides to get $-4y > 20$ , then divide by -4 and flip the inequality sign (since dividing by a negative number) to get $y < -5$ .

Practice 85 Inequalities questions in the app

Inequalities — ISEE Upper practice questions

Sample questions

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Mathematics Achievement