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All courses Math Foundations · MF.EQ.11 38 of 60
Solve multi-step inequalities, including reversing the inequality when appropriate.

Combine like terms before solving an inequality

Problem
Combine like terms on the left side, then solve the inequality: \(3x~+~5~+~x~>~17\)
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Hint

Start by combining the like terms on the left: the two x-terms go together, but the 5 stays separate.

Only like terms combine. After simplifying, solve the one-step inequality by undoing +5, then dividing by a positive coefficient, so the > direction stays the same.

Solution walkthrough

01

Combine like terms on the left

\[3x~+~x~=~(3~+~1)x~=~4x\]

Both terms share variable x, so their coefficients add.

02

Rewrite and isolate the variable term

\[4x~+~5~>~17;~4x~>~12\]

Subtracting 5 from both sides preserves the inequality direction.

03

Divide by positive four

\[x~>~12/4~=~3\]

Positive division does not reverse the greater-than symbol.

04

Check and report

\[x~>~3\]

At x = 3 the left side equals 17, so the strict boundary is excluded; larger values satisfy.

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Another way

  1. Find the strict boundary by solving the related equation 3x + 5 + x = 17, then test a value above it.

!

Common mistake

Do not treat 3x + x as 3x squared. Combining like terms adds coefficients and keeps the variable power unchanged.

Solution walkthrough video