The lesson
This lesson teaches Two-Step Equations. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
Work the order of operations in reverse
To get the variable alone, undo addition or subtraction first, then undo multiplication or 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.
An equation says two expressions have the same value. Whatever you do to one side, you must do to the other to keep the balance.
Check your solution by substituting it back into the original equation. If both sides match, your answer is correct.
Solve 2x + 5 = 13.
- 1Subtract 5 from both sides: 2x = 8.
- 2Divide both sides by 2: x = 4.
- 3Check: 2(4) + 5 = 13. ✓
An equation says two expressions have the same value. Whatever you do to one side, you must do to the other to keep the balance.
Check your solution by substituting it back into the original equation. If both sides match, your answer is correct.
Why this matters
Two-Step Equations shows up constantly in undo two operations to isolate the variable. It also connects to what you will see on homework, quizzes, and the next unit in this grade.
Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.
Common mistakes to avoid
Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.
Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.
Key ideas from this lesson
- Work the order of operations in reverse
Video walkthrough
Solving 2-Step Equations
Undo operations in reverse to isolate the variable.
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: x + 9 = 14.
Step-by-step solution
- 1Subtract 9 from both sides: x = 5.
Exercise 2
Try it yourselfSolve: 4x − 7 = 21.
Step-by-step solution
- 1Add 7: 4x = 28.
- 2Divide by 4: x = 7.
Exercise 3
Try it yourselfSolve: n/3 + 2 = 11.
Step-by-step solution
- 1Subtract 2: n/3 = 9.
- 2Multiply by 3: n = 27.
Exercise 4
Try it yourselfThree more than twice a number is 19. Write and solve an equation.
Step-by-step solution
- 1Equation: 2x + 3 = 19.
- 2Subtract 3: 2x = 16.
- 3Divide by 2: x = 8.
Exercise 5
Try it yourselfSolve: −5x + 12 = −3.
Step-by-step solution
- 1Subtract 12: -5x = -15.
- 2Divide by -5: x = 3.
- 3Check: -5(3) + 12 = -3 ✓
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Two-Step Equations
Question 1 of 4
Solve: 3x - 4 = 11.