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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 \(x~+~6~>~11\). Report the solution inequality with the correct boundary and inequality symbol.
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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

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

Six is added to x, so subtracting 6 will isolate the variable.

02

Subtract six from both sides

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

Subtracting the same number preserves the inequality direction.

03

Simplify the boundary

\[x~>~5\]

Eleven minus six is 5, and the strict greater-than sign remains unchanged.

04

Check and report

\[x~>~5\]

A value above 5, such as 6, gives 12 > 11; the boundary value 5 gives equality and is excluded.

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Another way

  1. Ask which x-values become greater than 11 after adding 6; they must start greater than 5.

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Common mistake

Do not reverse the inequality when subtracting 6. Reversal is required only when multiplying or dividing both sides by a negative number.

Solution walkthrough video