Learn with Amar
Teaching video
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Browse grades and teaching videos01 · Read and understand
What you will learn
- Write a grouped expression.
- Distribute a multiplier to every term.
- Verify equivalent expressions by substitution.
Before you start
Multiply whole numbers, substitute values, and identify like terms.
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
Each of three event kits contains two notebooks priced at x dollars each and one $4 folder. Write and expand the total-cost expression, then evaluate it when x = 5.
Why this math matters
Bundled costs can be written compactly or expanded into item totals. The distributive property connects these views. Both should count exactly the same items, which makes the physical bundle a useful check on symbolic algebra.
Set up the model
A useful answer starts with clear assumptions:
- All three kits are identical, and notebook prices match.
- The $4 folder price is per kit; no other costs 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.
Expand an event-kit cost without losing a term
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Each of three event kits contains two notebooks priced at x dollars each and one $4 folder. Write and expand the total-cost expression, then evaluate it when x = 5.
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.
Price one kit
one kit = 2x + 4 dollars
Two notebooks contribute twice the unknown price. The folder contributes a separate constant amount.
Repeat the entire kit
3(2x + 4) = 3(2x) + 3(4) = 6x + 12
Three kits contain six notebooks and three folders. Distributing only to 2x would leave two folders uncounted.
Evaluate both forms
3(2 × 5 + 4) = 42; 6 × 5 + 12 = 42
With $5 notebooks, either expression gives the same cost. The item-count reasoning establishes equivalence for every permitted notebook price, not only five.
The result
The total is 3(2x + 4) = 6x + 12 dollars; at x = 5, it is $42.
A single substitution is a useful error check, but agreement at one input does not prove two arbitrary expressions are identical. Here the distributive property supplies the general justification.
Common mistakes to catch
- The outside multiplier applies to the constant term too.
- 6x and 12 are unlike terms, so they cannot be combined into 18x.
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
Expand 4(x + 3) and evaluate it at x = 2.
Show a hint
Multiply both terms by four.
Reveal answer and explanation
4x + 12; value 20
Four copies of x + 3 give 4x + 12. Substituting two gives 8 + 12 = 20.
Practice 2
Simplify 5x + 3 + 2x − 1.
Show a hint
Group x terms together and constants together.
Reveal answer and explanation
7x + 2
5x + 2x = 7x, while 3 − 1 = 2. The variable and constant parts remain separate.
Take the idea with you
Draw repeated bundles before expanding an expression. Label the total count of each item to check every coefficient.
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: Find when two membership plans cost the same
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