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Two-Step Equations
A two-step equation like 3x + 5 = 20 takes two moves. Undo the adding or subtracting first, then undo the multiplying or dividing. It is the order of operations in reverse.
For: Grade 7 and 8 students and pre-algebra learners.
The rules
- Step 1: add or subtract to move the constant term to the other side.
- Step 2: multiply or divide to get the variable alone.
- Check by substituting your answer into the original equation.
Worked examples
Example 1: 3x + 5 = 20
- Subtract 5 from both sides: 3x = 15.
- Divide both sides by 3: x = 5.
- Check: 3(5) + 5 = 20 ✓
Answer: x = 5
Example 2: −2y − 7 = 9
- Add 7 to both sides: −2y = 16.
- Divide both sides by −2: y = −8.
- Check: −2(−8) − 7 = 16 − 7 = 9 ✓
Answer: y = −8
Example 3: x/4 + 3 = 7
- Subtract 3 from both sides: x/4 = 4.
- Multiply both sides by 4: x = 16.
- Check: 16/4 + 3 = 7 ✓
Answer: x = 16
Example 4: (2/3)n − 1 = 5
- Add 1 to both sides: (2/3)n = 6.
- Multiply both sides by 3/2: n = 9.
- Check: (2/3)(9) − 1 = 6 − 1 = 5 ✓
Answer: n = 9
Practice problems
- 4x − 3 = 21
- 5 + 2a = −11
- k/3 − 2 = 4
- −6m + 4 = 34
- (3/4)p + 2 = 11
Show answers
- x = 6
- a = −8
- k = 18
- m = −5
- p = 12
Frequently asked questions
Which step comes first in a two-step equation?
Usually undo the addition or subtraction first, then the multiplication or division.
What if the variable is on the right side?
Solve it the same way. For example, 17 = 2x + 3 gives 14 = 2x, so x = 7.
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