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 additional educational resources,. For education statistics and research, visit the National Center for Education Statistics.

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. For education statistics and research, visit the National Center for Education Statistics.

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: For education statistics and research, visit the National Center for Education Statistics.

• 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.

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Here is a step-by-step guide to solving one-step multiplication and division equations: For education statistics and research, visit the National Center for Education Statistics.

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. For education statistics and research, visit the National Center for Education Statistics.

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. For education statistics and research, visit the National Center for Education Statistics.

Step 3: Check your solution

Plug in your solution to the original equation to ensure it is correct. For education statistics and research, visit the National Center for Education Statistics.

Sample Questions of One-Step Multiplication and Division Equations

Examples 1 – solve the equation and graph the solution

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Solve the equation. And graph the solution, \(\frac{x}{2}=5\) For education statistics and research, visit the National Center for Education Statistics.

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. For education statistics and research, visit the National Center for Education Statistics.

Examples 2 – solve the equation and graph the solution

Solve the equation. And graph the solution \(9v=27\) For education statistics and research, visit the National Center for Education Statistics.

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.