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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 the equation 5x + 2 = 2x + 14. Write your answer as x = .
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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

Start with the given equation

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

The variable term appears on both sides, so the first goal is to collect the x-terms onto one side.

02

Move the smaller x-term off the right side

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

Subtracting 2x from both sides keeps the equation balanced and removes the x-term from the right side.

03

Combine like terms

\[3x~+~2~=~14\]

On the left, 5x - 2x becomes 3x. Now there is only one variable term to solve.

04

Isolate the variable term

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

Subtract 2 from both sides to undo the +2 next to 3x.

05

Solve for x

\[3x~=~12,~\text{so}~x~=~4\]

Divide both sides by 3. The solution is x = 4.

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Another way

  1. Check by substitution: 5(4) + 2 = 20 + 2 = 22 and 2(4) + 14 = 8 + 14 = 22. Both sides match, so x = 4 is correct.

!

Common mistake

A common mistake is subtracting 2x from only the left side and not the right side. You must do the same operation to both sides of 5x + 2 = 2x + 14 to keep the equation true.