Lesson 1: Solving Simple Equations

Property

An equation is a statement that two expressions are equal. It may involve one or more variables. A value of the variable that makes an equation true is called a solution of the equation, and the process of finding this value is called solving the equation.

Examples

• The statement $x + 5 = 12$ is an equation. The value $x=7$ is a solution because $7 + 5 = 12$ is a true statement.
• To check if $y=3$ is a solution to $8y = 24$, we substitute it in: $8(3) = 24$. This is true, so $y=3$ is a solution.
• Is $z=10$ a solution for $z - 4 = 5$? We check: $10 - 4 = 6$. Since $6$ is not equal to $5$, $z=10$ is not a solution.

Explanation

Think of an equation as a perfectly balanced scale. A solution is the specific value for the variable that keeps the scale level. Finding that value is what we call solving the equation.

Property

Multiplication and division are opposite or inverse operations, because each operation undoes the effects of the other.
Addition and subtraction are opposite or inverse operations, because each operation undoes the effects of the other.

Examples

• To undo adding 8, you subtract 8. For example, $x + 8 - 8$ simplifies back to just $x$.
• To undo multiplying by 3, you divide by 3. For example, $\frac{3y}{3}$ simplifies back to just $y$.
• The inverse of subtracting 10 is adding 10, and the inverse of dividing by 5 is multiplying by 5.

Explanation

Inverse operations are pairs of actions that cancel each other out, like locking and unlocking a door. We use them to isolate a variable by undoing whatever operation is being performed on it.