One-Step Multiplication Equations

Idea

A one-step multiplication equation has one multiplication attached to the variable. Your goal is to isolate the variable by using the opposite operation: division.

Method

1. Identify the factor multiplying the variable.
   • Example: in 5x = 30, the variable x is multiplied by 5.
2. Divide both sides by that number.
   • 5x ÷ 5 = 30 ÷ 5
3. Simplify.
   • x = 6

Signs and fractions

• If the coefficient is negative, divide carefully with signs.
  • Example: -3x = 12 gives x = -4.
• If the equation uses fractions, division still works the same way.

Check your answer

Substitute your value back into the original equation.

• For 5x = 30, check 5(6) = 30, which is true.

Helpful habit

After dividing, make sure the answer is fully simplified. If a number can be reduced, write it in simplest form. If the variable is on the right side, you can still divide both sides by the same factor to isolate it.