Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to undo operations in a two-step equation.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Addition, multiplication, and inverse operations.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A fictional craft session costs $9 plus $4 for each kit. The bill is $37. How many kits were purchased?
Why this math matters
Solving an equation preserves equality while undoing operations in reverse order. Translate a fixed amount plus repeated equal amounts into an equation before guessing the unknown count.
Set up the model
A useful answer starts with clear assumptions:
- The $9 fee occurs once.
- Kits have a constant $4 price and no other charges apply.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Undo operations in a two-step equation
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A fictional craft session costs $9 plus $4 for each kit. The bill is $37. How many kits were purchased?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
9 + 4k = 37
The fixed fee and variable kit charge add to the total.
Apply the relationship
4k = 28; k = 7
Subtract 9 from both sides, then divide both sides by 4.
Check and interpret
9 + 4(7) = 37, so 7 kits were purchased
The solution satisfies the original equation and is a whole-number count.
The result
9 + 4(7) = 37, so 7 kits were purchased
The solution satisfies the original equation and is a whole-number count.
Common mistakes to catch
- Dividing only one term on a side does not preserve the equation.
- Solving the arithmetic is not enough if the answer violates a counting restriction.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Solve 5x − 6 = 29.
Show a hint
Add 6 before dividing by 5.
Reveal answer and explanation
x = 7
5x = 35, then x = 7.
Practice 2
Write and solve an equation for three equal lengths plus a 2 cm margin totaling 20 cm.
Show a hint
Represent each equal length by l.
Reveal answer and explanation
3l + 2 = 20; l = 6 cm
Removing the margin leaves 18 cm shared equally among three lengths.
Take the idea with you
Translate a fixed amount plus repeated equal amounts into an equation before guessing the unknown count.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Reverse an inequality when dividing by a negative
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