Solving One- and Two-Step Equations
Solving Linear Equations
An equation is a statement that two expressions are equal. Solving an equation means finding the value of the unknown variable that makes the statement true. One-step and two-step equations are the simplest types, requiring just one or two inverse operations to isolate the variable.
The golden rule of equation solving is balance: whatever you do to one side, you must do to the other. This principle — rooted in the properties of equality — will carry you through every equation you ever solve, from basic algebra through differential equations.
This lesson teaches you to solve one-step equations (using addition, subtraction, multiplication, or division) and two-step equations (which combine two operations), building the mechanical fluency that more complex problems demand.
A linear equation in one variable has the form $ax + b = c$. The solution is the value of $x$ that makes the equation true.
Isolate the variable using inverse operations. Whatever you do to one side, do to the other.
One-Step Equations
$x + 7 = 12$
Subtract 7: $x = 12 - 7 = 5$. Check: $5 + 7 = 12$ ✓
$4x = 20$
Divide by 4: $x = 5$. Check: $4(5) = 20$ ✓
$\dfrac{x}{3} = 9$
Multiply by 3: $x = 27$. Check: $\dfrac{27}{3} = 9$ ✓
$x - 15 = -8$
Add 15: $x = -8 + 15 = 7$.
Two-Step Equations
Undo addition/subtraction first, then multiplication/division.
$3x + 7 = 22$
- Subtract 7: $3x = 15$
- Divide by 3: $x = 5$
Check: $3(5) + 7 = 22$ ✓
$\dfrac{x}{4} - 3 = 5$
- Add 3: $\dfrac{x}{4} = 8$
- Multiply by 4: $x = 32$
$-5x + 2 = -18$
- Subtract 2: $-5x = -20$
- Divide by $-5$: $x = 4$
Practice Problems
Show Answer Key
1. $x = 5$
2. $x = -6$
3. $x = 14$
4. $x = -20$
5. $x = 6$
6. $x = 24$
7. $x = 2$
8. $x = 5$
9. $x = -12$
10. $x = -5$
11. $x = 6$
12. $x = 8$
13. $x = 15$
14. $x = -12$
15. $x = 3$