How to Combine Like Terms Before Solving

Algebra 1 · Solving linear equations

How to Combine Like Terms Before Solving

Problem

5x - 3x + 4 = 14

Answer

x = 5

When the same variable appears more than once on one side, combine those terms first. The equation becomes shorter and easier to solve.

Step-by-step solution

Combine the x-terms on the left side.
$5x - 3x = 2x$
Why: Like terms have the same variable, so their coefficients subtract.
Rewrite the equation.
$2x + 4 = 14$
Why: The left side now has one x-term and one number.
Subtract 4 from both sides.
$2x = 10$
Why: Subtracting undoes the addition.
Divide both sides by 2.
$x = 5$
Why: Dividing undoes the multiplication.

Common mistakes

Combining 5x and 4. Only like terms can be added or subtracted.
Subtracting 3x from the right side as well. Combine before moving anything.
Dividing 10 by 5 instead of by 2.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

$7x - 2x + 3 = 18$

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$x = 3$
$4x + 6x - 5 = 35$

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$x = 4$
$9x - 4x + 2 = 22$

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$x = 4$
$3x + 5x - 4 = 12$

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$x = 2$
$6x - x + 7 = 32$

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$x = 5$