Algebra 1 / Unit 2: Solving Equations
2.3 Variables on Both Sides
Notes
Move the variable terms to one side and the constants to the other, then solve.
- $7x + 2 = 4x + 17 \Rightarrow 3x = 15 \Rightarrow x = 5$.
- If the variables cancel and you get a false statement like $3 = 8$, there is no solution.
- If you get a true statement like $3 = 3$, there are infinitely many solutions (an identity).
Practice
Solve $9a - 4 = 5a + 12$.
$4a = 16$.
How many solutions does $2(x + 3) = 2x + 6$ have?
Both sides are $2x + 6$, so every $x$ works.
How many solutions does $4x - 1 = 4x + 5$ have?
Subtracting $4x$ gives $-1 = 5$, which is false.
Ready for more? Take the Unit 2 test.