How to Solve and Graph One-Step Multiplication and Division Equations

Solving one-step equations is an important math skill to help students find the value of a variable that makes an equation true.

For example, consider the equation 4x = 12. To solve for x, you only need to divide both sides of the equation by 4, which gives you x = 3.

Steps to Solving & Graphing One-Step Multiplication and Division Equations

One-Step equations are ones that merely require one math operation to be solved.
You can use these four rules to solve one-step equations:

• Both sides stay equal if you add the same number to both sides of an equation.
• Both sides stay equal if you subtract the same number from both sides of an equation.
• Both sides stay equal if you divide both sides of an equation by the same number.
• Both sides stay equal if you multiply both sides of an equation by the same number.

Here is a step-by-step guide to solving one-step multiplication and division equations:

Step 1: Identify the variable and the operation

Determine which variable you are trying to solve for and identify whether the operation in the equation is addition, subtraction, multiplication, or division.

Step 2: Isolate the variable

Use inverse operations to isolate the variable on one side of the equation. If the operation is multiplication, divide both sides of the equation by the constant. If the operation is divided, multiply both sides of the equation by the constant.

Step 3: Check your solution

Plug in your solution to the original equation to ensure it is correct.

Sample Questions of One-Step Multiplication and Division Equations

Examples 1 – solve the equation and graph the solution

Solve the equation. And graph the solution, \(\frac{x}{2}=5\)

Solution

Use inverse operations for \(x\) to solve the equation.
Since x is divided by 2 in this equation, its inverse is multiplied by 2 on both sides. \(\frac{x}{2}×2=5×2→x=10\). Now, graph 10 on the number line.

Examples 2 – solve the equation and graph the solution

Solve the equation. And graph the solution \(9v=27\)

Solution

Use inverse operations for v to solve the equation.
Since v is multiplied by 9 in this equation, then its inverse is divided by 9 into both sides, \(\frac{9v}{9}=\frac{27}{9}→x=3\). Now, graph \(x=3\) on the number line.