Integrated Math 1 / Unit 2: Equations and Inequalities
2.1 Solving Linear Equations
Notes
To solve, use inverse operations on both sides to get the variable alone.
- Distribute and combine like terms on each side first.
- With variables on both sides, move the variable terms to one side and constants to the other.
- Clear decimals or fractions by multiplying every term by a power of 10 or the least common denominator.
- A false result like $6 = 5$ means no solution; a true result like $4 = 4$ means infinitely many solutions.
- Example: $4(x - 3) = 2x + 6 \Rightarrow 4x - 12 = 2x + 6 \Rightarrow 2x = 18 \Rightarrow x = 9$.
Practice
Solve $4(x - 3) = 2x + 6$.
$4x - 12 = 2x + 6$, so $2x = 18$ and $x = 9$.
Solve $\displaystyle \frac{2}{3}x - 4 = 8$.
Add 4: $\displaystyle \frac{2}{3}x = 12$. Multiply by $\displaystyle \frac{3}{2}$: $x = 18$.
Solve $0.5x + 1.2 = 0.2x + 3$.
Subtract $0.2x$ and $1.2$: $0.3x = 1.8$, so $x = 6$.
Ready for more? Take the Unit 2 test.