Solving Two-Step Equations
Solve equations requiring two inverse operations, applying them in the correct order (undo addition/subtraction before multiplication/division). Model real-world situations with two-step equations.
A lesson of Pre-Algebra, in Expressions & Equations, about 10 minutes.
Two-Step Equations
By the end of this lesson, you will be able to solve two-step equations by undoing operations in the correct order.
Strategy: Undo in Reverse PEMDAS Order
For equations like $ax + b = c$:
- First: undo the addition or subtraction (deal with the constant)
- Second: undo the multiplication or division (deal with the coefficient)
Examples
$3x + 7 = 22$
Step 1: Subtract 7: $3x = 15$
Step 2: Divide by 3: $x = 5$
Check: $3(5) + 7 = 22$ ✓
$\dfrac{n}{4} - 3 = 9$
Step 1: Add 3: $\dfrac{n}{4} = 12$
Step 2: Multiply by 4: $n = 48$
$-5y + 2 = -13$
Step 1: Subtract 2: $-5y = -15$
Step 2: Divide by −5: $y = 3$
Writing Two-Step Equations from Words
"Five more than three times a number is 20."
$3n + 5 = 20 \to 3n = 15 \to n = 5$
"Maria earns $12 per hour. After paying $9 in parking, she had $75. How many hours did she work?"
$12h - 9 = 75 \to 12h = 84 \to h = 7$ hours
Summary
Order of operations to undo: reverse PEMDAS — undo + or − first, then × or ÷.
Both steps must be applied to both sides.
Check: plug your answer back into the original equation.