Solving One-Step Equations

What Is an Equation?

An equation has an equal sign and says two expressions are equal: $x + 5 = 12$

Solving with Inverse Operations

To solve, undo the operation using its inverse:

| Operation | Inverse | |-----------|---------| | Addition | Subtraction | | Subtraction | Addition | | Multiplication | Division | | Division | Multiplication |

Addition Equations

$x + 5 = 12$ $x + 5 - 5 = 12 - 5$ $x = 7$ ✅

Check: $7 + 5 = 12$ ✓

Subtraction Equations

$n - 3 = 8$ $n - 3 + 3 = 8 + 3$ $n = 11$ ✅

Multiplication Equations

$4x = 20$ $\frac{4x}{4} = \frac{20}{4}$ $x = 5$ ✅

Division Equations

$\frac{x}{3} = 6$ $\frac{x}{3} \times 3 = 6 \times 3$ $x = 18$ ✅

The Balance Model

Think of an equation as a balance scale:

• Whatever you do to one side, you must do to the other
• The goal is to get the variable alone on one side

Writing Equations from Word Problems

"A number increased by 7 equals 15" $n + 7 = 15 \implies n = 8$

"Three times a number is 24" $3n = 24 \implies n = 8$

Always check your answer by substituting it back into the original equation!