Maths · Algebra Foundations
Two-step equations
Solve 3x + 5 = 20 style equations.
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What is a two-step equation?
A two-step equation needs two operations to solve it. For example, 3x + 5 = 20 has multiplication and addition. Our job is to find the value of x by doing the opposite operations in reverse order.
The golden rule: keep it balanced
An equation is like a balance scale. Whatever you do to one side, you must do to the other. If you subtract 5 from the left side, you must subtract 5 from the right side too.
Two steps: undo addition or subtraction first
Always undo addition or subtraction before multiplication or division. This is the reverse of the normal order of operations. Think of it as unwrapping a present: the last layer on goes off first.
Step one: deal with the constant
The constant is the number without a variable (letter). In 3x + 5 = 20, the constant is 5. Subtract 5 from both sides to get 3x = 15.
Step two: deal with the coefficient
The coefficient is the number multiplying the variable. In 3x = 15, the coefficient is 3. Divide both sides by 3 to get x = 5.
Worked examples
1. Solve 3x + 5 = 20
- Subtract 5 from both sides: 3x + 5 - 5 = 20 - 5
- Simplify: 3x = 15
- Divide both sides by 3: 3x ÷ 3 = 15 ÷ 3
- Solution: x = 5
2. Solve 2x - 7 = 11
- Add 7 to both sides: 2x - 7 + 7 = 11 + 7
- Simplify: 2x = 18
- Divide both sides by 2: 2x ÷ 2 = 18 ÷ 2
- Solution: x = 9
3. Solve 4x + 3 = 19
- Subtract 3 from both sides: 4x + 3 - 3 = 19 - 3
- Simplify: 4x = 16
- Divide both sides by 4: 4x ÷ 4 = 16 ÷ 4
- Solution: x = 4
Try it yourself
Solve 5x + 8 = 33
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