Pre-Algebra
Expressions and equations
Solving one-step equations
20 practice questions
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Theory + worked examples
Solving One-Step Equations
California Pre-Algebra • Standard 6.EE.7 • Expressions & Equations
Solving One-Step Equations is a topic in Expressions & Equations in the California Common Core State Standards. It is aligned to Standard 6.EE.7, which requires students to solve one-step equations using inverse operations.
A one-step equation is solved by applying one inverse operation to both sides.
Theory
A one-step equation needs a single operation to solve.
Undo the operation with its inverse, doing the same to both sides.
An equation is a balance.
Solving in one step.
Inverse operations:
\[+\leftrightarrow-,\qquad \times\leftrightarrow\div\]
Whatever you do to one side, do to the other.
How to solve a one-step equation
- Identify the operation on the variable.
- Apply its inverse to both sides.
- Simplify to isolate the variable.
- Check by substituting back.
Example 1 — Subtract
Solve \(x+4=9\).
Solution
Subtract \(4\) from both sides.
| \(x\) | \(=\) | \(5\) |
Example 2 — Add
Solve \(x-3=7\).
Solution
Add \(3\) to both sides.
| \(x\) | \(=\) | \(10\) |
Example 3 — Divide
Solve \(5x=20\).
Solution
Divide both sides by \(5\).
| \(x\) | \(=\) | \(4\) |
Example 4 — Multiply
Solve \(\dfrac{x}{3}=6\).
Solution
Multiply both sides by \(3\).
| \(x\) | \(=\) | \(18\) |
Common pitfalls
Do the same to both sides to stay balanced.
Use the inverse operation, not the same one.
Check your solution.
Frequently asked questions
What is a one-step equation?
An equation solved with one inverse operation.
How do I keep it balanced?
Do the same thing to both sides.
Solve \(x+4=9\).
\(x=5\).
Solve \(5x=20\).
\(x=4\).
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