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All courses Math Foundations · MF.EQ.6 33 of 60
Solve two-step equations and justify each inverse operation.

Solve a two-step equation with a constant and coefficient

Problem
Solve \(3x~+~5~=~20\).
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Hint

Look at the left side: the +5 is attached to 3x. Undo that first by subtracting 5 from both sides.

Use inverse operations in reverse order: remove the outside addition before undoing the multiplication by 3, or x will not be isolated.

Solution walkthrough

01

Undo the constant term first

\[3x~+~5~-~5~=~20~-~5\]

Subtracting 5 from both sides removes the addition attached after the product.

02

Simplify the equation

\[3x~=~15\]

The variable term is now isolated from the constant.

03

Undo multiplication by three

\[3x/3~=~15/3,~\text{so}~x~=~5\]

Dividing both sides by 3 leaves one x.

04

Check and report

\[x~=~5\]

Substitution gives 3(5) + 5 = 20, so the solution is correct.

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Another way

  1. Work backward from 20: subtract 5 to get 15, then divide by 3 to get 5.

!

Common mistake

Do not divide by 3 before accounting for the added 5 as though the right side alone were the product. Undo operations in reverse order.

Solution walkthrough video