Solving One-Step Equations

One-Step Equations

By the end of this lesson, you will be able to solve one-step equations using inverse operations and verify your solution.

The Goal

Isolate the variable: get the variable alone on one side of the equals sign by using the inverse operation.

Golden rule: whatever you do to one side, do to the other side.

The Four Types

Addition → subtract to undo:

$x + 9 = 14 \to x = 14 - 9 = 5$

Subtraction → add to undo:

$y - 6 = 11 \to y = 11 + 6 = 17$

Multiplication → divide to undo:

$4n = 28 \to n = 28 \div 4 = 7$

Division → multiply to undo:

$\dfrac{t}{5} = 8 \to t = 8 \times 5 = 40$

Solving with Negative Numbers

$x + 15 = 6 \to x = 6 - 15 = -9$

$-3m = 24 \to m = 24 \div (-3) = -8$

$\dfrac{x}{-4} = -7 \to x = (-7)(-4) = 28$

Checking Your Solution

Always substitute back into the original equation.

Check $x = 5$ in $x + 9 = 14$: $5 + 9 = 14$ ✓

Writing and Solving from Words

"A number decreased by 7 is 13." → $n - 7 = 13 \to n = 20$

"The product of a number and 6 is −42." → $6n = -42 \to n = -7$

Summary

Inverse operations: +↔−, ×↔÷.

Apply the inverse to both sides to isolate the variable.

Always check by substituting back into the original equation.