Start here

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: Clue: 'A bag holds fewer than 10 items.' What does 'fewer than' mean? It means less than, and it does NOT include 10, so we use <. We let n be the number of items: n < 10. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartSolve: 6x = 42

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

   How do you know?
3. 3

   Warm restartSolve: n / 3 = 8

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

   How do you know?
4. 4

   Warm restartSolve: 9m = 63

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

   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 throughWhich speed is NOT possible for the getaway car?

   1. A70 mph
   2. B65 mph
   3. C60 mph
   4. D45 mph

   Why is that the answer?
2. 6

   Think it throughDoes s ≤ 65 include 65 itself?

   1. AYes — the 'or equal to' part includes 65
   2. BNo — it must be strictly less
   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'?

   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'?

Use the words

Fill each blank with a word from the bank.

• Use <, >, ≤ or ≥ when the answer is a ___ of values rather than one.
• 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 ___.

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'?
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.

   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'?

   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

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

   How do you know?
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

   How do you know?

Be honest — this tells your teacher what to do next