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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: Let's simplify 5x + 3x. Are these like terms? Yes, both have x, so we add the numbers in front: 5 + 3 = 8. So 5x + 3x = 8x. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartExpand 5(x + 3).

   1. A5x + 15
   2. B5x + 3
   3. Cx + 15
   4. D8x

   How do you know?
3. 3

   Warm restartWhich shows 6n + 18 factored using its GREATEST common factor?

   1. A6(n + 3)
   2. B3(2n + 6)
   3. C2(3n + 9)
   4. D6(n + 18)

   How do you know?
4. 4

   Warm restartExpand 4(2y − 5).

   1. A8y − 20
   2. B8y − 5
   3. C6y − 20
   4. D2y − 20

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughSimplify (8m + 5) + (3m + 7) + (4m + 2).

   1. A15m + 14
   2. B15m + 15
   3. C29m
   4. D12m + 17

   Why is that the answer?
2. 6

   Think it throughWhat does the 15m tell the festival?

   1. A15 cables are needed for every microphone
   2. BThere are 15 microphones
   3. C15 stages need cables
   4. DThe cables cost $15

   How do you know? Give a second reason as well.
3. 7

   Think it throughIf each stage has 4 microphones (m = 4), how many cables in total?

   1. A74
   2. B60
   3. C64
   4. D29

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelWhat rule determines whether two terms are 'like terms'? Why can't you combine unlike terms?

Use the words

Fill each blank with a word from the bank.

• Combine ___ ___ to write a shorter expression with the same value.
• Terms with the same variable part, like 3y and 8y, are ___.
• To add or subtract like terms into a single term is to ___ them.
• Rewriting an expression in a shorter form that is still equal to it is to ___ it.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: A common mistake in Simplify Algebraic Expressions is sweeping a constant into the variable terms — for example, simplifying 6x + 4 + 2x as 12x by adding all three numbers (6 + 4 + 2 = 12) instead of recognizing that 4 has no variable and cannot combine with 6x and 2x.
2. 10

   Say moreTo simplify 6x + 4 + 2x + 7, which are the like terms, and how do you combine them?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A studio order lists the same equipment two different ways. On the left it is written out item by item — microphone, microphone, stand, microphone, stand. On the right the same gear is grouped together — 3 microphones and 2 stands.

   Show your work

Last check

These two come from Lesson 6.14. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Simplify 6x + 3 + 2x + 5.

   1. A8x + 8
   2. B8x² + 8
   3. C62x + 35
   4. D16x

   Explain your choice.
2. 13

   From Lesson 6.14Explain your thinking — Which expression is equivalent to 7(x + 3)?

   1. A7x + 21
   2. B7x + 3
   3. Cx + 21
   4. D7x + 10

   How do you know?
3. 14

   From Lesson 6.14A student wrote 8(12 + 9) = 8 × 12 + 9 = 105. What went wrong?

   1. AThey forgot to multiply the 9 by 8 as well
   2. BThey added instead of multiplying
   3. CThey used the wrong prices
   4. DThey distributed too many times

   How do you know?

Be honest — this tells your teacher what to do next