Properties of Equality

Addition: If $a = b$ then $a + c = b + c$. Subtraction: If $a = b$ then $a c = b c$. Multiplication: If $a = b$ then $ac = bc$. Division: If $a = b$ and $c \neq 0$ then $\frac{a}{c} = \frac{b}{c}$.

To solve $x 8 = 10$, use the Addition Property: $x 8 + 8 = 10 + 8$, which simplifies to $x = 18$.\nTo solve $4y = 24$, use the Division Property: $\frac{4y}{4} = \frac{24}{4}$, which simplifies to $y = 6$.\nTo solve $ 2x + 5 = 15$, first subtract 5: $ 2x = 10$. Then divide by 2: $x = 5$.

Imagine an equation is a perfectly balanced seesaw. To keep it level, whatever you do to one side, you must do the exact same thing to the other. Whether you add, subtract, multiply, or divide by a number, applying the action to both sides ensures the equation remains true, helping you isolate the variable and solve the puzzle.