Pre-Algebra
Expressions and equations
Solving two-step equations
20 practice questions
0 video lessons
Theory + worked examples
Solving Two-Step Equations
California Pre-Algebra • Standard 7.EE.4 • Expressions & Equations
Solving Two-Step Equations is a topic in Expressions & Equations in the California Common Core State Standards. It is aligned to Standard 7.EE.4, which requires students to solve two-step equations in one variable.
A two-step equation is solved by undoing addition or subtraction first, then multiplication or division.
Theory
A two-step equation takes two inverse operations to solve.
Undo add/subtract first, then undo multiply/divide — the reverse of the order of operations.
A two-step equation.
The order of steps.
The reverse order:
\[\text{undo }\pm\ \text{ first, then }\times\text{ or }\div\]
Reverse the order of operations to solve.
How to solve a two-step equation
- Add or subtract to isolate the variable term.
- Multiply or divide to isolate the variable.
- Simplify each side.
- Check the solution.
Example 1 — Standard
Solve \(2x+3=11\).
Solution
Subtract \(3\), then divide by \(2\).
| \(2x\) | \(=\) | \(8\) |
| \(x\) | \(=\) | \(4\) |
Example 2 — Subtraction
Solve \(3x-5=16\).
Solution
Add \(5\), then divide by \(3\).
| \(3x\) | \(=\) | \(21\) |
| \(x\) | \(=\) | \(7\) |
Example 3 — Division form
Solve \(\dfrac{x}{2}+1=5\).
Solution
Subtract \(1\), then multiply by \(2\).
| \(\dfrac{x}{2}\) | \(=\) | \(4\) |
| \(x\) | \(=\) | \(8\) |
Example 4 — Negative
Solve \(-2x+7=1\).
Solution
Subtract \(7\), then divide by \(-2\).
| \(-2x\) | \(=\) | \(-6\) |
| \(x\) | \(=\) | \(3\) |
Common pitfalls
Undo addition first, then the coefficient.
Divide the whole side, not just one term.
Watch signs when dividing by a negative.
Frequently asked questions
What is a two-step equation?
An equation needing two inverse operations.
Which step comes first?
Undo addition or subtraction first.
Solve \(2x+3=11\).
\(x=4\).
Solve \(3x-5=16\).
\(x=7\).
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