Start here

Use the model to solve the first problem. Then try these quick review questions from earlier lessons.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step. 🔊 Listen 💡 Hint

   Try it together — then prove it:

   1. Are 2x + 3x and 5x equivalent? Test x = 2. Then explain why they always match.
   2. Substitute x = 2 into both expressions. (2 × 2 + 3 × 2 = 10 and 5 × 2 = 10)
   3. Combine the like terms in 2x + 3x. (2x + 3x is 5x.)
   4. Why does 2x + 3x match 5x for every x, not just 2? (2 groups of x plus 3 groups of x is 5 groups of x. That is true for any number x.)

   Show your work
2. 2

   Quick reviewEvaluate 4n + 3 when n = 5. 🔊 Listen 💡 Hint

   1. A23
   2. B27
   3. C35
   4. D45

   How do you know?
3. 3

   Quick reviewWhich expression means '7 more than a number x'? 🔊 Listen 💡 Hint

   1. Ax + 7
   2. B7x
   3. Cx − 7
   4. D7 − x

   How do you know?
4. 4

   Quick reviewA ticket costs $9. Which expression gives the cost of t tickets? 🔊 Listen 💡 Hint

   1. A9t
   2. Bt + 9
   3. C9 + t
   4. Dt ÷ 9

   How do you know?

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughSimplify 4h + 2h + 30. 🔊 Listen 💡 Hint

   1. A4h + 32
   2. B6h + 30
   3. C6h + 30h
   4. D36h

   Why is that the answer?
2. 6

   Think it throughAre the two pricing formulas equivalent? 🔊 Listen 💡 Hint

   1. AYes — 4h + 2h + 30 simplifies to exactly 6h + 30
   2. BNo — Client A pays more
   3. CNo — Client B pays more
   4. DOnly when h = 0

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

   Think it throughTest it: what does each expression equal when h = 5? 🔊 Listen 💡 Hint

   1. AA = 50 and B = 60
   2. BBoth equal 60
   3. CA = 60 and B = 55
   4. DBoth equal 90

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

   Back to the modelHow did you decide which expressions belong in the same group? What strategies did you use? 🔊 Listen 💡 Hint

Use the words

Fill each blank with a word from the bank.

• Expressions with the same value for ___ allowed number are equivalent.
• Expressions that always have the same value are ___.
• Rewriting an expression in a shorter form that is still equal to it is to ___ it.
• Terms with the same variable raised to the same power, like 4x and 9x, are ___.

Explain the thinking

1. 9

   Find the mistakeRead the mistake. Explain what went wrong, then show the correct step. 🔊 Listen 💡 Hint

   The mistake: A common mistake in Equivalent Expressions is adding the exponents instead of the coefficients when combining like terms — writing 3x + 2x as 5x² instead of 5x.
2. 10

   Say moreHow can you prove 2(n + 4) and 2n + 8 are equivalent? What two strategies could you use? 🔊 Listen 💡 Hint
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: The same square is shown two ways — broken into green strips and yellow unit squares on the left, and as one whole red square on the right. 🔊 Listen 💡 Hint

   Show your work

Last check

These two come from Lesson 6.5. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Which expression is equivalent to 6n + 4 + 3n − 1? 🔊 Listen 💡 Hint

   1. A9n + 3
   2. B9n + 5
   3. C18n + 4
   4. D63n

   Explain your choice.
2. 13

   From Lesson 6.5Explain your thinking — A club orders one $4.25 shirt for each student plus a one-time $23.50 shipping fee. Write the expression for s students, then find the cost for 30 students. 🔊 Listen 💡 Hint

   1. A4.25s + 23.50; for s = 30 the cost is $151.00
   2. B4.25s + 23.50; for s = 30 the cost is $832.50
   3. C4.25 + 23.50s; for s = 30 the cost is $709.25
   4. D27.75s; for s = 30 the cost is $832.50

   How do you know?
3. 14

   From Lesson 6.5In 25 + 8h, what is the coefficient? 🔊 Listen 💡 Hint

   1. A25
   2. B8
   3. Ch
   4. D25h

   How do you know?

Check your progress

Choose the box that best describes how you feel about each skill.