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All courses Math Foundations · MF.EQ.10 37 of 60
Solve one-step inequalities and represent solutions on a number line.

Solve an additive one-step inequality

Problem
Solve the inequality x + 6 > 11. Write your answer as a solved inequality.
Your answer
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Hint

Look at the +6 attached to x. Undo it by subtracting 6 from both sides of the inequality.

Solve one-step inequalities like equations: use the inverse operation on both sides. The inequality symbol stays the same when you add or subtract the same number.

Solution walkthrough

01

Identify the operation on x

\[x~+~6~>~11\]

The variable x has 6 added to it. To isolate x, undo +6 by subtracting 6 from both sides.

02

Subtract 6 from both sides

\[x~+~6~-~6~>~11~-~6\]

Subtracting the same number from both sides keeps the inequality balanced.

03

Simplify both sides

\[x~>~5\]

On the left, +6 and -6 cancel, leaving x. On the right, 11 - 6 = 5.

04

State the solution set

\[x~>~5\]

The solved inequality is x > 5, so the solution set is all numbers greater than 5.

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Another way

  1. Use the boundary idea: x = 5 makes x + 6 equal 11. Since the inequality needs a value greater than 11, x must be greater than 5.

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Common mistake

Changing > to < after subtracting 6. The inequality direction stays the same when you add or subtract the same amount on both sides; it only flips when multiplying or dividing by a negative.