The lesson
Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
Using inverse operations
An equation says two things are equal. To solve for the variable, undo the operation attached to it by doing the opposite to BOTH sides. Addition is undone by subtraction, multiplication by division.
A ratio compares two quantities with the same units. Order matters: a ratio of cats to dogs is not the same as dogs to cats unless the problem says they are equivalent.
Write ratios in three ways: with a colon (3:4), as a phrase (3 to 4), or as a fraction (3/4) when it fits the context.
Solve x + 7 = 15
- 1The +7 is attached to x, so subtract 7 from both sides.
- 2x + 7 − 7 = 15 − 7.
- 3x = 8.
Always check your answer
Substitute your answer back into the original equation. If both sides match, you got it right.
Why this matters
Undo whatever is happening to the variable to find its value.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Doing different operations to each side of an equation. Whatever you add, subtract, multiply, or divide on one side, do to the other.
Combining unlike terms (like 3x and 4) as if they were the same kind of term.
Key ideas from this lesson
- Using inverse operations
- Always check your answer
Video walkthroughs
Solving Basic Algebraic Equations
Add, subtract, multiply, or divide both sides to isolate x.
Watch on YouTube
Solving 2-Step Equations
Undo two operations in reverse order to isolate the variable.
Watch on YouTube
Two-Step Equations with Decimals and Fractions
Solve equations that include rational number coefficients.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfSolve for x: x + 9 = 17.
Step-by-step solution
- 1Subtract 9 from both sides.
- 2x = 17 − 9 = 8.
Exercise 2
Try it yourselfSolve for n: n − 6 = 11.
Step-by-step solution
- 1Add 6 to both sides.
- 2n = 11 + 6 = 17.
Exercise 3
Try it yourselfSolve for y: 4y = 28.
Step-by-step solution
- 1Divide both sides by 4.
- 2y = 28 ÷ 4 = 7.
Exercise 4
Try it yourselfSolve for m: m/5 = 9.
Step-by-step solution
- 1Multiply both sides by 5.
- 2m = 9 × 5 = 45.
Exercise 5
Try it yourselfAfter buying a $12 book, Maya has $23 left. Write and solve an equation for how much money m she started with.
Step-by-step solution
- 1Equation: m − 12 = 23.
- 2Add 12 to both sides: m = 35.
- 3Check: 35 − 12 = 23.
Worksheet - Equations & inequalities
Mixed practice solving equations and inequalities.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
One-Step Equations
Question 1 of 5
Solve for x: x + 7 = 12