Middle school · Mathematics · 20 minutes
Solve and Check an Equation
Use inverse operations on both sides to solve a one-variable equation.
Middle School Math Foundations · Lesson 3 · Starter collectionLearning objective
Use inverse operations on both sides to solve a one-variable equation.
Gather your materials
- Paper or notebook
- Pencil; a calculator for checking arithmetic when appropriate
The lesson time covers the core activity. Allow extra time for video viewing and extended discussion.
Common Core skill focus
7.EE.B.4.aStandard level: Grade 7
Represent a situation with a simple equation and solve it while preserving equality.
Read the official standard ↗Compare the equation method with an arithmetic solution in the teaching steps. Code and level checked 2026-11-04; selected skill coverage.
Teach it step by step
- Ask what the learner already knows. Introduce the objective and read the explanation together.
- Work through the example aloud. Pause for the learner to explain why each step or piece of evidence matters.
- Choose a video if useful, then connect it to the example. Let the learner complete the independent practice before checking the explained answers.
- Discuss the question below and finish with the exit check. Revisit the example if the reasoning is unclear.
Watch, notice, discuss
Video choices for this lesson
Preview a video, then choose what fits your learners. “Show to class” opens a larger view; use the player’s play and full-screen controls when you’re ready.
Teacher preview needed. Check the language, level and length before showing. YouTube may show ads or related videos.
How to Solve Two-Step Equations | Math with Mr. J
By Math with Mr. J
Use this explanation as an introduction, then pause to connect it to the worked example and discussion question.
Open on YouTube: How to Solve Two-Step Equations | Math with Mr. J (opens a new tab) ↗Solving Equations | Algebra | Math with Mr. J
By Math with Mr. J
Compare this alternate explanation with the lesson. Ask learners to show their reasoning after watching.
Open on YouTube: Solving Equations | Algebra | Math with Mr. J (opens a new tab) ↗Why must the same operation happen on both sides? Check your answer in the original equation.
An external player loads only after you choose Preview or Show to class. Playback connects to YouTube. Videos belong to their creators; availability and embedding can change.
Understand the idea
An equation states that two expressions have equal value. To preserve equality, perform the same operation on both sides. Undo addition or subtraction, then multiplication or division, as needed. Combining like terms first can simplify the work. Substitution into the original equation checks the answer and catches sign errors.
Worked example
Solve 3x + 5 = 20. Subtract 5 from both sides: 3x = 15. Divide both sides by 3: x = 5. Check: 3(5) + 5 = 20. In a context, if three equal tickets and a $5 fee cost $20, each ticket costs $5.
Try it yourself
- Solve 4x − 7 = 13.
- Solve 2(x + 3) = 18.
- Write and solve an equation: a $6 fee plus $4 per visit totals $30.
Check your reasoning
- 4x = 20, so x = 5. Check: 4(5) − 7 = 13.
- Divide by 2 to get x + 3 = 9, then x = 6.
- 6 + 4v = 30; 4v = 24; v = 6 visits.
Make it work for your learner
For support, model the example one step at a time and ask the learner to explain each choice in their own words. Use a sketch, organizer or physical model where helpful. For a challenge, create a new example, test an alternative explanation or describe when the model would not apply.
Exit check
Use inverse operations on both sides to solve a one-variable equation. Explain your reasoning with a specific example before moving on.
Compare with arithmetic
For three tickets and a $5 fee totaling $20, an arithmetic solution is (20 − 5) ÷ 3 = 5 dollars per ticket. Compare each operation with the algebraic solution of 3x + 5 = 20. Why do both methods give the same answer?
Prepare · Discuss · Reflect
Use evidence in a conversation
Discussion question: Why must the same operation happen on both sides? Check your answer in the original equation.
- Before discussing, write a tentative answer with two details from the lesson’s passage, example or data. For a longer discussion, the teacher can add an age-appropriate source.
- In pairs, a group or a tutor–learner conversation, agree on roles: facilitator, evidence finder and note taker. Combine roles when needed and allow equal time to respond.
- Share evidence, ask a clarifying question and respond to a different interpretation. Explain which details support or challenge a claim.
- Paraphrase another person’s point. Write a final conclusion explaining what changed, what remains uncertain and what evidence you would seek next.
Teacher look-for: Accurate use of the example, reasons linked to evidence, thoughtful questions and a response to another viewpoint. A well-supported alternative answer is welcome.