How to Solve a Two-Step Linear Equation
An equation says two expressions have the same value. A variable such as x stands for a number. Solving means finding the value that makes the equation true.
The Big Idea
Think of an equation as a balanced scale. Doing the same valid operation to both sides keeps the sides equal. The goal is to leave the variable by itself.
Work Through an Example
Solve 3x + 5 = 20.
Subtract 5 from both sides: 3x + 5 − 5 = 20 − 5.
Why: The +5 is outside the multiplication by 3. Undo that addition first. Subtracting only on the left would change the balance.
Simplify: 3x = 15.
Why: Adding 5 and then subtracting 5 cancels out. On the right, 20 − 5 = 15. Now three equal groups of x have a total of 15.
Divide both sides by 3: x = 5.
Why: Dividing 3x by the nonzero number 3 undoes multiplication by 3. One group must be 15 ÷ 3 = 5.
Check in the original equation: 3(5) + 5 = 20.
Why: The left side becomes 15 + 5 = 20, matching the right side. That confirms x = 5 works.
A Common Mix-Up
Avoid saying a number simply “moves across and changes sign.” The sign change comes from adding or subtracting the same amount on both sides. Also, never divide by zero.
Try Another Way to Picture It
Three identical notebooks plus a $5 pen cost $20. Remove the pen cost: the notebooks cost $15 together. Split $15 equally among 3 notebooks: each notebook costs $5.
Your Turn
Try these on paper, then open each answer to check your reasoning. These examples do not record a score or change your learning progress.
Solve 4x − 7 = 9.
Show answer and explanation
x = 4
Add 7 on both sides to get 4x = 16. Divide by 4. Check: 4(4) − 7 = 9.
Solve −2x + 6 = 14.
Show answer and explanation
x = −4
Subtract 6 on both sides to get −2x = 8. Divide by −2. Check: −2(−4) + 6 = 14.
Keep This in Mind
Undo the addition or subtraction, then the multiplication or division. Do each operation to both sides, and check in the original equation.