Introduction
Solving Two-Step Equations is an important Grade 7 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with solving two-step equations.
What Is Solving Two-Step Equations?
Solving Two-Step Equations means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Solving Two-Step Equations
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: Find \(x\) using the step-by-step table:
| Step | Equation |
|---|---|
| Original | \(3x+5=20\) |
| Subtract 5 | \(3x=15\) |
| Divide by 3 | \(x=?\) |
- A. \(x=3\)
- B. \(x=5\)
- C. \(x=9\)
- D. \(x=15\)
Why it works: From the table, \(3x=15\), so dividing both sides by \(3\) gives \(x=5\).
Answer: \(x=5\)
Visual Model 2
Question: Solve: \(-3x+8=2\)
- A. \(x=1\)
- B. \(x=2\)
- C. \(x=3\)
- D. \(x=4\)
Why it works: Subtract \(8\): \(-3x=-6\). Divide by \(-3\): \(x=2\).
Answer: \(x=2\)
Worked Examples
Example 1
Question: Solve: \(\frac{2x}{3}+4=10\)
- A. \(x=6\)
- B. \(x=9\)
- C. \(x=12\)
- D. \(x=15\)
- Subtract \(4\): \(\frac{2x}{3}=6\).
- Multiply by \(\frac{3}{2}\): \(2x=18 \Rightarrow x=9\).
Answer: \(x=9\)
Example 2
Question: Solve: \(-2x-7=1\)
- A. \(x=-4\)
- B. \(x=-2\)
- C. \(x=2\)
- D. \(x=4\)
- Add \(7\): \(-2x=8\).
- Divide by \(-2\): \(x=-4\).
Answer: \(x=-4\)
Example 3
Question: What is the solution to \(7x+4=32\)? (Check by substitution.)
- A. \(x=3\)
- B. \(x=4\)
- C. \(x=5\)
- D. \(x=6\)
- Subtract \(4\): \(7x=28\).
- Divide by \(7\): \(x=4\).
- Check: \(7(4)+4=28+4=32\) ✓.
Answer: \(x=4\)
Real-World Word Problems
Problem 1
Question: Marcus saves money each week. He already has $15 and saves $8 per week. After how many weeks will he have $63?
- A. 4 weeks
- B. 6 weeks
- C. 8 weeks
- D. 10 weeks
Why it works: Set up: \(8w+15=63 \Rightarrow 8w=48 \Rightarrow w=6\).
Answer: 6 weeks
Problem 2
Question: A shirt costs $35 and socks cost $4 per pair. If you buy 1 shirt and \(p\) pairs of socks for a total of $51, how many pairs of socks did you buy?
- A. 2 pairs
- B. 4 pairs
- C. 6 pairs
- D. 8 pairs
Why it works: Set up: \(35+4p=51 \Rightarrow 4p=16 \Rightarrow p=4\).
Answer: 4 pairs
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
Solve for \(x\): \(2x+7=19\)
- A. \(x=4\)
- B. \(x=5\)
- C. \(x=6\)
- D. \(x=13\)
Question 2
Solve: \(2(x+3)=14\)
- A. \(x=2\)
- B. \(x=3\)
- C. \(x=4\)
- D. \(x=7\)
Question 3
Which value of \(x\) satisfies \(4x+2=18\)?
- A. \(x=2\)
- B. \(x=4\)
- C. \(x=5\)
- D. \(x=8\)
Question 4
Solve for \(y\): \(5y-3=22\)
- A. \(y=3\)
- B. \(y=5\)
- C. \(y=19\)
- D. \(y=25\)
Question 5
What is \(x\) if \(3(x-2)=9\)?
- A. \(x=2\)
- B. \(x=3\)
- C. \(x=5\)
- D. \(x=6\)
Question 6
Find \(x\): \(\frac{x}{2}+3=7\)
- A. \(x=4\)
- B. \(x=6\)
- C. \(x=8\)
- D. \(x=10\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(x=6\)
Subtract \(7\): \(2x=12\). Divide by \(2\): \(x=6\).
Question 2
Answer: \(x=4\)
Divide by \(2\): \(x+3=7\). Subtract \(3\): \(x=4\).
Question 3
Answer: \(x=4\)
Subtract \(2\): \(4x=16\). Divide by \(4\): \(x=4\).
Question 4
Answer: \(y=5\)
Add \(3\): \(5y=25\). Divide by \(5\): \(y=5\).
Question 5
Answer: \(x=5\)
Divide by \(3\): \(x-2=3\). Add \(2\): \(x=5\).
Question 6
Answer: \(x=8\)
Subtract \(3\): \(\frac{x}{2}=4\). Multiply by \(2\): \(x=8\).
Connection to Standards
This lesson supports Grade 7 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Solving Two-Step Equations becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
