Study on the fly ISEE Upper Mathematics AchievementInequalities

Mathematics Achievement

Inequalities — ISEE Upper practice questions

47 questions on the paper
85 practice questions in the app
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Practice 85 Inequalities questions in the app

What this topic is

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.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

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

x < -\dfrac{11}{3}

x > 7

✗ Not this one

-7 < x < \dfrac{11}{3}

✗ Not this one

-\dfrac{11}{3} < x < 7

✓ Correct

x < 7

✗ Not this one

Show answer

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 2Easier

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

-2<x\le3

✓ Correct

-2\le x<3

✗ Not this one

x\le-2

x>3

✗ Not this one

2<x\le17

✗ Not this one

Show answer

Answer: A — $-2<x\le3$

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

Question 3Easier

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

y > -5

✗ Not this one

y < -5

✓ Correct

y > 5

✗ Not this one

y < 5

✗ Not this one

Show answer

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 $y < -5$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 85 Inequalities questions in the app

Inequalities — ISEE Upper practice questions

What this topic is

Sample questions

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Mathematics Achievement