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Teaching video
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Grade 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to solve an equation that needs distribution.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Distributive property and two-step equations.
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
Solve 3(2x − 1) + 4 = 25, then verify the solution in the original expression.
Why this math matters
Distributing and combining like terms can reveal the simpler equation hidden inside parentheses. Organize a multi-step equation into distribution, collection, isolation, and a final substitution check.
Set up the model
A useful answer starts with clear assumptions:
- x is real.
- Every algebraic operation is applied equally to both sides.
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.
Solve an equation that needs distribution
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Solve 3(2x − 1) + 4 = 25, then verify the solution in the original expression.
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
6x − 3 + 4 = 25; 6x + 1 = 25
Distribute 3 to both terms and combine the constants.
Apply the relationship
6x = 24; x = 4
Subtract 1, then divide by 6.
Check and interpret
3(2×4 − 1) + 4 = 3(7) + 4 = 25
The original parentheses evaluate correctly, confirming x = 4.
The result
3(2×4 − 1) + 4 = 3(7) + 4 = 25
The original parentheses evaluate correctly, confirming x = 4.
Common mistakes to catch
- An outside factor multiplies every term in its parentheses.
- Verify using the original equation so an early simplification error can be detected.
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 2(y + 5) − 3 = 19.
Show a hint
Distribute before combining constants.
Reveal answer and explanation
y = 6
2y + 7 = 19 gives 2y = 12, so y = 6.
Practice 2
Find the error in expanding −2(x − 4) as −2x − 8.
Show a hint
Multiply −2 by the negative constant.
Reveal answer and explanation
The constant should be +8
(−2)(−4) = +8, so the expansion is −2x + 8.
Take the idea with you
Organize a multi-step equation into distribution, collection, isolation, and a final substitution check.
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: Compare two expressions with the same unknown
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