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All courses Algebra I · A-REI.3 9 of 76
Solve linear equations and inequalities in one variable, including literal linear equations.

Solve a one- or two-step linear equation

Problem
Solve the linear equation \(3x~+~4~=~19\).
Your answer
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Hint

Undo the +4 first by subtracting 4 from both sides.

After subtracting 4, divide both sides by 3 to isolate x.

Solution walkthrough

01

Identify the operation structure

\[3x+4=19;~x~\text{is}~\text{multiplied}~by~3,~\text{then}~4~\text{is}~\text{added}\]

To isolate x, undo the outer addition before undoing multiplication, while applying each operation to both sides.

02

Undo the addition

\[3x+4-4=19-4~->~3x=15\]

Subtracting 4 from both sides removes the constant without changing the solution set.

03

Undo the multiplication

\[3x/3=15/3~->~x=5\]

Dividing both sides by the nonzero coefficient 3 isolates x and gives 5.

04

Check in the original equation

\[3(5)+4=15+4=19\]

The left side evaluates to the original right side, so no algebraic error was introduced.

05

State the solution

\[x~=~5\]

The verified solution exactly matches choice A.

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Another way

  1. Work backward from 19: subtract 4 to get 15, then ask which number multiplied by 3 equals 15.

!

Common mistake

Do not divide 19 by 3 before removing the added 4. Reverse the operations in order: subtract 4, then divide by 3.

Solution walkthrough video