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One-Step Equations
A one-step equation needs just one move to get the variable by itself. Do the opposite (inverse) operation to both sides, and always check your answer by putting it back in.
For: Grade 6 and 7 students starting algebra.
The rules
- If a number is added to x, subtract it from both sides.
- If a number is subtracted from x, add it to both sides.
- If x is multiplied by a number, divide both sides by it.
- If x is divided by a number, multiply both sides by it.
Worked examples
Example 1: x + 7 = 12
- Subtract 7 from both sides.
- x = 12 − 7.
- Check: 5 + 7 = 12 ✓
Answer: x = 5
Example 2: y − 4 = −9
- Add 4 to both sides.
- y = −9 + 4.
- Check: −5 − 4 = −9 ✓
Answer: y = −5
Example 3: 6n = 42
- Divide both sides by 6.
- n = 42 ÷ 6.
- Check: 6 × 7 = 42 ✓
Answer: n = 7
Example 4: m/3 = 8
- Multiply both sides by 3.
- m = 8 × 3.
- Check: 24 ÷ 3 = 8 ✓
Answer: m = 24
Practice problems
- x + 15 = 32
- a − 6 = 2
- −4k = 28
- p/5 = −3
- 9 = t + 11
Show answers
- x = 17
- a = 8
- k = −7
- p = −15
- t = −2
Frequently asked questions
What is an inverse operation?
The operation that undoes another one: subtraction undoes addition, and division undoes multiplication.
Why do you do the same thing to both sides?
An equation is like a balanced scale. Doing the same thing to both sides keeps it balanced, so the answer stays correct.
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