Inequalities — SHSAT practice questions

Inequalities on the SHSAT Mathematics section cover writing and solving comparison statements that use less than, greater than, or the inclusive versions of those relations. A student must translate a word problem, such as a budget for buying items, into an inequality, solve a linear inequality, and count the integers or positive integers that satisfy it. The exam typically asks which inequality represents a situation or how many integer values work. Traps include reversing the inequality when multiplying by a negative, mixing open and closed signs, and counting the wrong set of integers. Choices usually show rival inequalities or possible counts.

Section: Mathematics 57 questions on the paper
114 practice questions in the app

Sample questions

Question 1

How many integers $x$ satisfy $-2<\dfrac{x-5}{3}\le4$ ?

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Answer: C — 18

Multiplying by 3 gives $-6<x-5\le12$ . Adding 5 gives $-1<x\le17$ , so $x$ can be any integer from 0 through 17. There are 18 integers.

Question 2

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

A $3n \le 15$
B $3n \ge 15$
C $n + 3 \le 15$
D $15n \le 3$

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Answer: A — $3n \le 15$

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

Question 3

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

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Answer: B — 4

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

Practice 114 Inequalities questions in the app

Inequalities — SHSAT practice questions

Sample questions

More SHSAT topics

Mathematics