Inequalities — SHSAT practice questions

122 practice questions in the app
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Practice 122 Inequalities questions in the app

What this topic is

An inequality describes a range of values rather than a single answer, and it is solved like an equation with one key exception: multiplying or dividing both sides by a negative number reverses the direction of the sign.

Inequalities questions often ask how many integers, or how many positive integers, make a statement true, so the boundary values must be checked to see whether they are included. Word problems use phrases such as at most, which means less than or equal to, and at least, which means greater than or equal to.

Budget situations are a classic case, where the total cost must not exceed the money available.

Sample questions

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

Question 1Mid

How many integers $x$ satisfy $- 2 < \frac{x - 5}{3} \leq 4$ ?

16✗ Not this one17✗ Not this one18✓ Correct19✗ Not this one

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Answer: C — 18

Multiplying by 3 gives $- 6 < x - 5 \leq 12$ . Adding 5 gives $- 1 < x \leq 17$ , so $x$ can be any integer from 0 through 17. There are 18 integers.

Question 2Easier

Maya has $15 to spend on notebooks that cost $3 each. Which inequality represents $n$ , the number of notebooks she can buy?

3 n \leq 15

✓ Correct

3 n \geq 15

✗ Not this one

n + 3 \leq 15

✗ Not this one

15 n \leq 3

✗ Not this one

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Answer: A — $3 n \leq 15$

Each notebook costs $3, so $n$ notebooks cost $3 n$ dollars, which must be at most 15: $3 n \leq 15$ .

Question 3Mid

How many positive integers $x$ satisfy $2 x - 3 < 7$ ?

3✗ Not this one4✓ Correct5✗ Not this one6✗ Not this one

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Answer: B — 4

$2 x - 3 < 7$ gives $2 x < 10$ , so $x < 5$ . The positive integers less than 5 are $1, 2, 3, 4$ , which is 4 values.

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

Practice 122 Inequalities questions in the app

Inequalities — SHSAT practice questions

What this topic is

Sample questions

More SHSAT topics

Mathematics