Study on the fly ISEE Upper Mathematics AchievementInequalities

Mathematics Achievement

Inequalities — ISEE Upper practice questions

90 practice questions in the app
Free

Practice 90 Inequalities questions in the app

What this topic is

What sets Inequalities apart from equations is one rule: multiplying or dividing both sides by a negative number reverses the inequality sign.

Forgetting that flip is the most frequent error, and its result is nearly always among the answer choices. Absolute value inequalities add a second idea: an absolute value less than a number means the expression lies between that number and its opposite, so the absolute value of x being less than five means x is between negative five and five.

Questions ask for a solution set, an equivalent inequality, or a graph on a number line. Open and closed circles show whether endpoints are included.

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 $∣ 3 x - 5 ∣ < 16$ ?

x < - \frac{11}{3}

x > 7

✗ Not this one

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

✗ Not this one

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

✓ Correct

x < 7

✗ Not this one

Show answer

Answer: C — $- \frac{11}{3} < x < 7$

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

Question 2Easier

Which inequality is equivalent to $- 2 < 3 x + 4 \leq 13$ ?

- 2 < x \leq 3

✓ Correct

- 2 \leq x < 3

✗ Not this one

x \leq - 2

x > 3

✗ Not this one

2 < x \leq 17

✗ Not this one

Show answer

Answer: A — $- 2 < x \leq 3$

Subtracting 4 gives $- 6 < 3 x \leq 9$ . Dividing by 3 gives $- 2 < x \leq 3$ .

Question 3Easier

If $- 4 y + 7 > 27$ , 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 $- 4 y > 20$ , 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 90 Inequalities questions in the app

Inequalities — ISEE Upper practice questions

What this topic is

Sample questions

More ISEE Upper topics

Mathematics Achievement