If 4y − 9 = 11, what is y?

Two-step linear equation. Add 9 to both sides: 4y − 9 + 9 = 11 + 9, giving 4y = 20. Divide both sides by 4: 4y ÷ 4 = 20 ÷ 4, giving y = 5. Verify: 4(5) − 9 = 20 − 9 = 11 ✓. The algorithm: undo operations in reverse order of operations. The original expression performs (1) multiply variable by 4, then (2) subtract 9. To solve, reverse: first add 9 (undo subtraction), then divide by 4 (undo multiplication). For more complex equations with variables on both sides: first move all variables to one side (by adding/subtracting), then constants to the other, then solve. Example: 3x + 5 = 2x − 8 → x + 5 = −8 → x = −13. Variables in equations represent unknown quantities; solving identifies the value(s) that satisfy the equation.