Pre-Algebra

Solving One-Step Inequalities

Lesson

An inequality uses $<$ , $>$ , $\le$ , or $\ge$ instead of an equals sign. Solving works almost the same as a one-step equation — with one important twist.

Apply the inverse operation to both sides, just like an equation. But:

The flip rule

When you multiply or divide both sides by a negative number, you must flip the inequality symbol. $<$ becomes $>$ , and $\le$ becomes $\ge$ .

You don’t flip when you add or subtract — only when you multiply or divide by a negative.

Worked example 1

x + 3 < 10

Subtract 3 from both sides:

x < 7

Worked example 2

-2x \ge 8

Divide both sides by $-2$ . Because we divided by a negative, the inequality flips:

x \le -4

How to type your answer

Write your answer in the form $x$ + symbol + number. Use <, >, <=, or >=. Examples: x<7, x>-4, x>=10.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

x + 1 < 4

Problem 2

x - 2 > 0

Problem 3

2x < 8

Problem 4

\frac{x}{2} > 3

Practice

Standard problems matching the lesson.

Problem 5

x + 3 < 10

Problem 6

x - 5 > 2

Problem 7

x + 8 \le 4

Problem 8

x - 1 \ge -3

Problem 9

3x < 15

Problem 10

5x \ge 20

Problem 11

\frac{x}{2} > 6

Problem 12

\frac{x}{4} \le -1

Problem 13

-2x < 10

Problem 14

-3x \ge 12

Problem 15

\frac{x}{-2} > 4

Problem 16

-x \le 5

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 17

x - 11 \ge -4

Problem 18

x + 7 \le -2

Problem 19

7x \ge -49

Problem 20

-5x < 25

Problem 21

-x > -8

Problem 22

\frac{x}{-5} \ge 2