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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.

   Let's do one together: Clue: "A bag holds fewer than 10 items." Write an inequality for the number of items. What does "fewer than" mean? (Less than.) Can the bag hold exactly 10 items? (No. 10 is not fewer than 10, so 10 is not included.) Which symbol do we use? (<) Let n be the number of items. Write the inequality. (n < 10)

   My first step is ___ , because the problem asks for ___ .

   Show your work
2. 2

   Warm restartSolve: 6x = 42

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

   Warm restartSolve: n / 3 = 8

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

   Warm restartSolve: 9m = 63

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

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 throughWhich speed is NOT possible for the getaway car?

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

   Why is that the answer?

   I chose ___ because ___ .
2. 6

   Think it throughDoes s ≤ 65 include 65 itself?

   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?

   I chose ___ because ___ .
3. 7

   Think it throughWhich inequality means 'at most 65'?

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

   Explain your thinking.

   I chose ___ because ___ .
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'?

   'At least' uses ≥ instead of > because it means the value ___ be equal to the number, while 'more than' means it must be ___.

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 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 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'?

   'At least' uses ___ because it ___ the number, but 'more than' uses ___.
3. 11

   Change one numberGo back to Part 1 and pick one problem you already solved. Change one number in it, then solve your new version. Show every step.

   If ___ changed to ___ , then ___ .

   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 knowQuick check — you've got this: Which inequality represents: 'A number n is at least 14'?

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

   Explain your choice.

   I know it is ___ because ___ .
2. 13

   From Lesson 8.3Quick check — you've got this: Solve: w / 8 = 6

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

   From Lesson 8.3Check: does 9 work?

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

Be honest — this tells your teacher what to do next