Two-step equations are algebraic equations that require two inverse operations to isolate the variable and calculate its value. Typically, these equations involve a sequence of operations, such as addition or subtraction followed by multiplication or division. For example, to solve 2x+3=11, subtract 3 from both sides and then divide by 2.
Practicing two-step equations through various problems and worksheets helps reinforce this process. Resources like this articles offers numerous practice problems and step-by-step solutions that guide you through solving these equations.
Solution of Two-Step Equations
Some general solutions for two-step equations are listed in the following table:
| Type of Equation | Example | Step 1 | Solution | Step 2 | Solution |
|---|---|---|---|---|---|
| Addition Equations | ax + b = c | Subtract b from both sides | ax + b - b = c - b ⇒ ax = c | Divide both sides b | x = c/a |
| Subtraction Equations | ax − b = c | Add b to both sides | ax - b + b = c + b ⇒ ax = c | Divide both sides by a | x = c/a |
| Multiplication Equations | x/a − b = c | Add b to both sides | x/a - b + b = c + b ⇒ x/a = c | Multiply both sides by a | x = ac |
Two-Step Equations Practice Questions with Solution
Question 1: Solve 2x + 8 = 16
Solution:
Subtract 8 from both sides:
2x + 8 - 8 = 16 - 8
⇒ 2x = 16
Divide both sides by 2:
2x/2 = 16/2
⇒ x = 8
Question 2: Solve 5x - 10 = 60
Solution:
Add 10 to both sides:
5x - 10 + 10 = 60 + 10
⇒ 5x = 70
Divide both sides by 5:
5x/5 = 70/5
⇒ x = 14
Question 3: Solve x/3 - 5 = 1
Solution:
Add 5 to both sides:
x/3 - 5 + 5 = 1 + 5
⇒ x/3 = 6
Multiply both sides by 3:
x/3 x 3 = 6 x 3
⇒ x = 18
Question 4: Solve 8x + 18 = -14
Solution:
Subtract 18 from both sides:
8x + 18 - 18 = -14 - 18
⇒ 8x = -32
Divide both sides by 8:
8x/8 = -32/8
⇒ x = -4
Question 5: Solve 6x - 12 = -30
Solution:
Add 12 to both sides:
6x - 12 + 12 = -30 + 12
⇒ 6x = -18
Divide both sides by 6:
6x/6 = -18/6
⇒ x = -3
Question 6: Solve 3x/2 + 4 = 10
Solution:
Subtract 4 from both sides:
3x/2 + 4 - 4 = 10 - 4
⇒ 3x/2 = 6
Multiply both sides by 2/3:
(3x/2) x 2/3= 6 x 2/3
⇒ x = 4
Question 7: Solve 4x - 6 = 2
Solution:
Add 6 to both sides:
4x - 6 + 6 = 2 + 6
⇒ 4x = 8
Divide both sides by 4:
4x/4 = 8/4
⇒ x = 2
Question 8: Solve 2x + 3 = 11
Solution:
Subtract 3 from both sides:
2x + 3 - 3 = 11 - 3
⇒ 2x = 8
Divide both sides by 2:
2x/2 = 8/2
⇒ x = 4
Two-Step Equations Practice Questions
Q1: Solve 5x + 10 = 40
Q2: Solve 2x - 4 = 20
Q3: Solve 6x + 5 = 35
Q4: Solve 2x/3 - 1 = 5
Q5: Solve x/2 + 3 = 9
Q6: Solve 13x - 26 = -13
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