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All courses Math Foundations · MF.EQ.8 35 of 60
Solve linear equations with variables on both sides and interpret special cases.

Collect variable terms on one side

Problem
Solve \(5x~+~2~=~2x~+~14\).
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Hint

Start by getting the x-terms on one side. Subtract 2x from both sides of 5x + 2 = 2x + 14.

When a variable appears on both sides, do the same operation to both sides so the equation stays balanced, then combine like terms.

Solution walkthrough

01

Move variable terms to one side

\[5x~+~2~-~2x~=~2x~+~14~-~2x\]

Subtracting 2x from both sides preserves equality and removes the right-side variable term.

02

Simplify and remove the constant

\[3x~+~2~=~14;~3x~=~14~-~2~=~12\]

Combine the left variable terms, then subtract 2 from both sides.

03

Divide by the coefficient

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

Dividing both sides by 3 isolates x.

04

Check and report

\[x~=~4\]

The left side is 5(4) + 2 = 22 and the right side is 2(4) + 14 = 22.

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Another way

  1. Subtract 5x instead, solve the equivalent equation 2 = -3x + 14, and obtain the same x = 4.

!

Common mistake

When subtracting 2x from 5x, the result is 3x, not 7x. The operation applies to both equation sides.

Solution walkthrough video