Solving Two-Step Equations
Grade 7 · Math · Study Guide
Use inverse operations in the right order to solve equations that require two steps to isolate the variable.
A two-step equation is an equation where you need exactly two operations to get the variable alone on one side. The goal is always the same: isolate the variable. You do this by undoing what was done to it, using inverse operations — addition undoes subtraction, multiplication undoes division, and vice versa.
The order matters. When solving, work in the reverse order of operations (PEMDAS in reverse). That means you undo addition or subtraction first, then undo multiplication or division. For example, to solve 2x + 5 = 17, first subtract 5 from both sides (2x = 12), then divide both sides by 2 (x = 6). Whatever you do to one side, you must do to the other to keep the equation balanced.
Think of an equation as a balance scale. Both sides must always be equal. Every operation you apply to one side must be applied to the other. This is the golden rule of algebra: maintain balance at every step.
You can always check your answer by substituting it back into the original equation. If both sides are equal, you have the right answer. For x = 6: 2(6) + 5 = 12 + 5 = 17. Correct!
Two-step equations set the stage for all future algebra. Every equation you will ever solve — from simple lines to complex quadratics — builds on the idea of isolating a variable using inverse operations. Getting these mechanics automatic now saves enormous effort later.
| Equation | Step 1 (undo + or −) | Step 2 (undo × or ÷) | Solution |
|---|---|---|---|
| 2x + 5 = 17 | 2x + 5 − 5 = 17 − 5 → 2x = 12 | 2x ÷ 2 = 12 ÷ 2 | x = 6 |
| 3x − 4 = 11 | 3x − 4 + 4 = 11 + 4 → 3x = 15 | 3x ÷ 3 = 15 ÷ 3 | x = 5 |
| x/4 + 2 = 7 | x/4 + 2 − 2 = 7 − 2 → x/4 = 5 | x/4 × 4 = 5 × 4 | x = 20 |
| Operation | Inverse Operation |
|---|---|
| Addition (+) | Subtraction (−) |
| Subtraction (−) | Addition (+) |
| Multiplication (×) | Division (÷) |
| Division (÷) | Multiplication (×) |
Key terms
- Two-step equation
- An equation that requires exactly two operations to isolate the variable
- Inverse operations
- Operations that undo each other: addition/subtraction and multiplication/division are inverse pairs
- Isolate the variable
- Get the variable alone on one side of the equals sign
- Balance principle
- Whatever you do to one side of an equation, you must do to the other side
- Solution
- The value of the variable that makes the equation true
Practice questions
What is the first step to solve 3x + 6 = 18?
- Divide both sides by 3
- Subtract 6 from both sides
- Add 6 to both sides
- Multiply both sides by 3
Show answer
Answer: Subtract 6 from both sides
Solve: 5x − 3 = 22. The value of x is ___.
Show answer
Answer: 5
To solve a two-step equation, you can perform the operations in any order and still get the correct answer.
Show answer
Answer: False
Which value of x solves x/2 + 4 = 10?
- 3
- 7
- 12
- 28
Show answer
Answer: 12
You can check your solution by substituting the value back into the original equation.
Show answer
Answer: True
Fun facts
- Equations have been solved symbolically since the 9th century, when Persian mathematician Al-Khwarizmi wrote the first algebra textbook — his name is the root of the word 'algorithm.'
- Architects use two-step equations to figure out how much material they need: if the total cost is known and the base fee is fixed, they solve for the per-unit cost.
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