The lesson
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.
Solve 2x + 5 = 13.
- 1Subtract 5 from both sides: 2x = 8.
- 2Divide both sides by 2: x = 4.
- 3Check: 2(4) + 5 = 13. ✓
Why this matters
Undo two operations to isolate the variable.
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
Reversing the order named in the problem. Write the ratio in the same order the words give you.
Treating a part-to-part ratio like a part-to-whole fraction without checking what the whole is.
Key ideas from this lesson
- Work the order of operations in reverse
Video walkthroughs
Solving 2-Step Equations
Undo operations in reverse to isolate the variable.
Watch on YouTube
One-Step Equations
Review inverse operations before tackling two-step equations.
Watch on YouTube
Two-Step Equations with Decimals and Fractions
Solve two-step equations with rational 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: 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.