How to Solve One-Step Equations? (+FREE Worksheet!)

Related Topics

• How to Solve Multi-Step Equations
• How to Solve One-Step Inequalities
• How to Solve Multi-Step Inequalities
• How to Solve Systems of Equations
• How to Graph Single–Variable Inequalities

Step by step guide to solve one–step equations

• The values of two expressions on both sides of an equation are equal. \(ax \ + \ b=c\)
• You only need to perform one Math operation in order to solve the one-step equations.
• To solve one-step equation, find the inverse (opposite) operation is being performed.
• The inverse operations are:
  Addition and subtraction
  Multiplication and division

One–Step Equations – Example 1:

Solve this equation. \(2x=16, x=?\)

Solultion:

Here, the operation is multiplication (variable \(x\) is multiplied by \(2\)) and its inverse operation is division. To solve this equation, divide both sides of equation by \(2\):
\(2x=16→ 2x \ ÷ \ 2=16 \ ÷ \ 2→x=8\)

One–Step Equations – Example 2:

Solve this equation. \(x \ + \ 12=0, x=?\)

Solultion:

Here, the operation is addition and its inverse operation is subtraction. To solve this equation, subtract \(12\) from both sides of the equation: \(x \ + \ 12=0\) → \(x \ + \ 12 \ − \ 12=0 \ − \ 12 \)
Then simplify: \(x \ + \ 12 \ − \ 12=0 \ − \ 12 → x=− 12 \)

One–Step Equations – Example 3:

Solve this equation. \( x+24=0 ,x=\) ?

Solution:

Here, the operation is addition and its inverse operation is subtraction. To solve this equation, subtract \(24\) from both sides of the equation: \( x+24=0\) → \(x+24-24=0-24 \)
Then simplify: \(x+24-24=0-24 → x=-24 \)

One–Step Equations – Example 4:

Solve this equation. \( 3x=15,x=\)?

Solution:

Here, the operation is multiplication (variable \(x\) is multiplied by \(3\)) and its inverse operation is division. To solve this equation, divide both sides of the equation by \(3\):
\( 3x=15→3x÷3=15÷3→x=5\)

Exercises for Solving One–Step Equations

Solve each equation.

• \(\color{blue}{x + 3 = 17}\)
• \(\color{blue}{22 = (– 8) + x}\)
• \(\color{blue}{3x = (– 30)}\)
• \(\color{blue}{(– 36) = (– 6x)}\)
• \(\color{blue}{(– 6) = 4 + x}\)
• \(\color{blue}{2 + x = (– 2)}\)

Download One-Step Equations Worksheet

Answers

• \(\color{blue}{14}\)
• \(\color{blue}{30}\)
• \(\color{blue}{-10}\)
• \(\color{blue}{6}\)
• \(\color{blue}{-10}\)
• \(\color{blue}{-4}\)