Algebra 1 / Unit 2: Solving Equations
2.2 Multi-Step Equations
Notes
Undo operations in reverse order: first addition or subtraction, then multiplication or division.
- Simplify each side first: distribute and combine like terms.
- Example: $3(x - 2) + 4 = 19 \Rightarrow 3x - 6 + 4 = 19 \Rightarrow 3x - 2 = 19 \Rightarrow 3x = 21 \Rightarrow x = 7$.
- To clear fractions, multiply every term by the least common denominator.
Practice
Solve $5x - 8 = 27$.
Add 8: $5x = 35$, so $x = 7$.
Solve $2(3k + 1) - k = 22$.
$6k + 2 - k = 22 \Rightarrow 5k = 20$.
Solve $\displaystyle \frac{x}{3} + \frac{1}{2} = \frac{5}{6}$.
Multiply by 6: $2x + 3 = 5$, so $x = 1$.
Ready for more? Take the Unit 2 test.