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Worksheet #482731

Algebra practice

Basic Inequalities

Name Date

x + 7 ≤ 25
x − 7 < −17
x + 9 ≤ 16
x − 11 < 3
−11x < 165
11x ≥ 77
10x ≤ −150
x − 2 ≤ −4
x − 7 < −10
3x > −3
x + 1 > 19
x + 10 < 21
x − 6 ≥ 10
2x ≥ 18
x − 9 ≥ −18
−5x ≥ −70
9x > −144
7x < −56
x + 2 < 10
7x ≥ −56

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Answer key

Verified answers

Basic Inequalities

Worksheet #482731

x + 7 ≤ 25x ≤ 18
x − 7 < −17x < −10
x + 9 ≤ 16x ≤ 7
x − 11 < 3x < 14
−11x < 165x > −15
11x ≥ 77x ≥ 7
10x ≤ −150x ≤ −15
x − 2 ≤ −4x ≤ −2
x − 7 < −10x < −3
3x > −3x > −1
x + 1 > 19x > 18
x + 10 < 21x < 11
x − 6 ≥ 10x ≥ 16
2x ≥ 18x ≥ 9
x − 9 ≥ −18x ≥ −9
−5x ≥ −70x ≤ 14
9x > −144x > −16
7x < −56x < −8
x + 2 < 10x < 8
7x ≥ −56x ≥ −8

Learn the skill

What is basic inequalities?

An inequality compares values using <, ≤, >, or ≥. Its solution is usually a range of numbers rather than one value.

How to solve basic inequalities

Use inverse operations to isolate the variable.
Reverse the inequality sign after multiplying or dividing by a negative number.
Test a value from the solution range in the original inequality.

Worked example

−2x < 10

Divide both sides by −2.
Reverse < to > because the divisor is negative.

Answer: x > −5

Common mistakes

Forgetting to reverse the sign after dividing by a negative.
Reversing the sign after adding or subtracting a number.
Giving one number instead of describing the solution range.

Practice tips

Circle any negative number used to multiply or divide.
Check one value that should work and one that should not.