Practice Inequality Intuition in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Understanding that << and >> describe ordering relationshipsβ€”one quantity is strictly smaller or larger than the other.

If 5<75 < 7, then 5 is somewhere to the left of 7 on the number line.

Showing a random 20 of 50 problems.

Example 1

medium
Solve 2(x+1)≀3xβˆ’42(x+1) \leq 3x - 4.

Example 2

medium
A car uses up to 1212 gallons per trip and contains gg gallons. Write an inequality for safe fuel.

Example 3

easy
Does x≀5x \le 5 include the value 55?

Example 4

easy
What does x≠3x \neq 3 mean?

Example 5

medium
Order from least to greatest: βˆ’32,Β 0.5,Β βˆ’1,Β 2-\frac{3}{2},\ 0.5,\ -1,\ 2.

Example 6

medium
Solve 3xβˆ’1β‰₯83x - 1 \ge 8.

Example 7

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Solve βˆ’3x≀9-3x \leq 9.

Example 8

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Explain why a<ba < b implies a+c<b+ca + c < b + c for any real cc.

Example 9

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Solve 5βˆ’x≀25 - x \le 2.

Example 10

easy
Rewrite 7>x7 > x with the variable on the left.

Example 11

medium
Which integers satisfy βˆ’1<x≀3-1 < x \le 3?

Example 12

medium
Solve βˆ’2xβ‰₯8-2x \geq 8 and explain the direction flip when multiplying by a negative.

Example 13

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How many positive integers nn satisfy n<7n < 7?

Example 14

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A student must score at least 70 to pass. They have scores 65, 72, 80. Which scores pass? Write as inequalities.

Example 15

easy
Solve 2xβˆ’4>62x - 4 > 6.

Example 16

easy
Translate: 'a price pp no more than $50' as an inequality.

Example 17

easy
Read 5≀y5 \leq y in words and rewrite with the variable on the left.

Example 18

easy
Solve x+3<10x + 3 < 10 and graph the solution on a number line.

Example 19

medium
Solve x2+1<4\frac{x}{2} + 1 < 4.

Example 20

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Which of the following violates ∣x∣<3|x| < 3: x=2.9x = 2.9, x=3x = 3, x=βˆ’2x = -2?