1.1Solving One-Step Equations
Use inverse operations to isolate the variable and solve addition, subtraction, multiplication, and division equations. Always check your solution.
Why This Matters
Solving equations is the single most important skill in all of algebra. You'll use it in every math and science course — from finding unknown forces in Physics to solving for concentrations in Chemistry.
Workbook
Lesson, vocabulary, worked examples, and practice problems.
Essential Question
How can we use inverse operations to find the value of an unknown?
Lesson Overview
An equation is a mathematical statement that two expressions are equal. A solution is the value of the variable that makes the equation true. To solve a one-step equation, we apply one inverse operation — the opposite of the operation shown — to both sides of the equation. This keeps the equation balanced and isolates the variable.
Worked Examples
Solve: x + 8 = 15
Identify the operation: addition (+8)
Apply the inverse: subtract 8 from both sides
x + 8 − 8 = 15 − 8
x = 7
Check: 7 + 8 = 15 ✓
Solve: x − 12 = 4
Identify the operation: subtraction (−12)
Apply the inverse: add 12 to both sides
x − 12 + 12 = 4 + 12
x = 16
Check: 16 − 12 = 4 ✓
Solve: 5x = 45
Identify the operation: multiplication (×5)
Apply the inverse: divide both sides by 5
5x ÷ 5 = 45 ÷ 5
x = 9
Check: 5(9) = 45 ✓
Solve: x/6 = 8
Identify the operation: division (÷6)
Apply the inverse: multiply both sides by 6
(x/6) × 6 = 8 × 6
x = 48
Check: 48/6 = 8 ✓
Solve: −3x = 21
Identify the operation: multiplication (×−3)
Apply the inverse: divide both sides by −3
−3x ÷ (−3) = 21 ÷ (−3)
x = −7
Check: −3(−7) = 21 ✓
Guided Practice
Guided Practice Video: Solving One-Step Equations
Watch the guided practice walkthrough for one-step equations, then complete the problems below.
Video by Sang Real Math
Watch on YouTube ↗Answers are in the Answer Key section.
Solve: n + 14 = 22
Hint: What operation is being done to n? Use the inverse to undo it.
Solve: y − 9 = 3
Hint: The operation is subtraction. Add 9 to both sides.
Solve: 7m = 56
Hint: m is being multiplied by 7. Divide both sides by 7.
Solve: x/4 = 12
Hint: x is being divided by 4. Multiply both sides by 4.
Solve: −6x = 42
Hint: Divide both sides by −6. Watch the sign of your answer.
Key Vocabulary
Equation
A mathematical statement showing two expressions are equal, connected by an equals sign (=).
Example: x + 5 = 12 is an equation.
Solution
The value of the variable that makes the equation true.
Example: x = 7 is the solution to x + 5 = 12.
Inverse Operation
The opposite operation used to undo another. Addition ↔ Subtraction; Multiplication ↔ Division.
Example: To undo +8, subtract 8 from both sides.
Variable
A letter representing an unknown number.
Example: In 3x = 15, x is the variable.
Isolate
To get the variable alone on one side of the equation.
Example: In x + 4 = 9, subtract 4 to isolate x.
Check
Substitute your answer back into the original equation to verify it is correct.
Example: If x = 7, check: 7 + 5 = 12 ✓
Practice Questions
Interactive Practice — 5 Questions
What is the solution to x + 9 = 21?
Which inverse operation solves 7x = 56?
What is the solution to y − 14 = 3?
Solve: −4x = −28
A student solved x + 5 = 13 and got x = 18. What mistake did they make?
Independent Practice
Answers are in the Answer Key section.
Independent Practice
Solve: x + 6 = 19
Solve: y − 11 = 5
Solve: 8n = 64
Solve: x/5 = 7
Solve: −4a = 36
Common Mistakes
Performing the operation on only one side — e.g., x + 5 = 12, subtracting 5 from only the left side.
Apply the inverse operation to BOTH sides: x + 5 − 5 = 12 − 5 → x = 7.
Using the same operation instead of the inverse — e.g., solving x + 5 = 12 by adding 5.
Use the inverse: addition undoes subtraction, multiplication undoes division.
Dividing by the wrong number — e.g., solving −4x = 20 by dividing by 4 instead of −4.
Divide by the coefficient including its sign: −4x = 20 → x = 20 ÷ (−4) = −5.
Forgetting to check the solution by substituting back into the original equation.
Always verify: substitute your answer back in and confirm both sides are equal.
Math Tips
Think of an equation as a balance scale. Whatever you do to one side, you must do to the other — otherwise the scale tips and the equation is no longer true.
Memorize the four inverse pairs: +/−, −/+, ×/÷, ÷/×. When you see the operation on the variable, apply its inverse to both sides.
Always check your answer. Substitute it back into the original equation. If both sides are equal, you are correct. This takes 5 seconds and catches most errors.
SAT/ACT tip: one-step equations appear in almost every section. Practice until solving them is automatic — you should not need to write out every step on the test.