Lesson 6: Solving One-Step Equations

Property

An expression is a mathematical phrase that contains numbers, variables, and operations but has no equal sign: $3x + 5$ or $2y - 7$.

An equation is a mathematical sentence that shows two expressions are equal using an equal sign: $3x + 5 = 14$ or $2y - 7 = 11$.

Property

To solve equations, we apply the rules of equivalence to isolate the variable.
For equations in the form $x + p = q$, we find the solution by subtracting $p$ from both sides.
For equations in the form $x - p = q$, we find the solution by adding $p$ to both sides.
All numbers $p$, $q$, and $x$ are integers or rational numbers.

Examples

Property

To solve equations involving multiplication or division, we apply the multiplication and division properties of equality to isolate the variable.
For equations in the form $ax = b$, we divide both sides by $a$ (where $a \neq 0$) to get $x = \frac{b}{a}$.
For equations in the form $\frac{x}{a} = b$, we multiply both sides by $a$ to get $x = ab$.

Examples