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. Clue: "A bag holds fewer than 10 items." Write an inequality for the number of items n.
   2. What does "fewer than" mean? Is 10 included? (It means less than. 10 is not included.)
   3. Write the inequality. (n < 10)
   4. Why is n ≤ 10 wrong for this clue? (n ≤ 10 includes 10. But a bag with 10 items does not hold fewer than 10.)

   Show your work
2. 2

   Quick reviewSolve: 6x = 42 🔊 Listen 💡 Hint

   1. Ax = 7
   2. Bx = 36
   3. Cx = 48
   4. Dx = 252

   How do you know?
3. 3

   Quick reviewSolve: n / 3 = 8 🔊 Listen 💡 Hint

   1. An = 3
   2. Bn = 5
   3. Cn = 11
   4. Dn = 24

   How do you know?
4. 4

   Quick reviewSolve: 9m = 63 🔊 Listen 💡 Hint

   1. Am = 7
   2. Bm = 54
   3. Cm = 72
   4. Dm = 567

   How do you know?

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughWhich speed is NOT possible for the getaway car? 🔊 Listen 💡 Hint

   1. A45 mph
   2. B60 mph
   3. C65 mph
   4. D70 mph

   Why is that the answer?
2. 6

   Think it throughDoes s ≤ 65 include 65 itself? 🔊 Listen 💡 Hint

   1. ANo — it must be strictly less
   2. BYes — the 'or equal to' part includes 65
   3. COnly if the car stops
   4. DOnly on a highway

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

   Think it throughWhich inequality means 'at most 65'? 🔊 Listen 💡 Hint

   1. As ≤ 65
   2. Bs < 65
   3. Cs ≥ 65
   4. Ds > 65

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

   Back to the modelHow do the words 'at least' and 'at most' change the inequality symbol compared to 'more than' and 'fewer than'? 🔊 Listen 💡 Hint

Use the words

Fill each blank with a word from the bank.

• A math sentence comparing values with <, >, ≤, or ≥ is an ___.
• The symbol > that means one value is larger than another means ___.
• The symbol < that means one value is smaller than another means ___.
• 'At least' means greater than or equal to, and 'at most' means ___ than or equal to.

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 Write Inequalities is using a strict symbol (> or <) for a phrase that actually includes the boundary value.
2. 10

   Say moreHow do the phrases 'at least' and 'at most' change which inequality symbol you choose compared to 'more than' and 'fewer than'? 🔊 Listen 💡 Hint
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Three balance scales are shown. On two of them the pans hang at different heights, so one side is heavier. On the third the pans are level. 🔊 Listen 💡 Hint

   Show your work

Last check

These two come from Lesson 8.3. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Which inequality represents: 'A number n is at least 14'? 🔊 Listen 💡 Hint

   1. An ≥ 14
   2. Bn > 14
   3. Cn ≤ 14
   4. Dn < 14

   Explain your choice.
2. 13

   From Lesson 8.3Explain your thinking — Solve: w / 8 = 6 🔊 Listen 💡 Hint

   1. Aw = 0.75
   2. Bw = 2
   3. Cw = 14
   4. Dw = 48

   How do you know?
3. 14

   From Lesson 8.3Check: does 9 work? 🔊 Listen 💡 Hint

   1. AYes — 7 × 9 = 63
   2. BNo — 7 × 9 = 56
   3. CNo — 7 + 9 = 16
   4. DOnly if kits cost $9

   How do you know?

Check your progress

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