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: 'The lookout earned less than $50.' Equation or inequality? 'Less than' is a limit, so it is an inequality. Let e be the earnings. 'Less than 50' means e < 50. Is $30 a reasonable value? Yes. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartSolve: x − 4 < 11

   1. Ax < 7
   2. Bx > 15
   3. Cx = 15
   4. Dx < 15

   How do you know?
3. 3

   Warm restartSolve: x + 6 > 14

   1. Ax > 20
   2. Bx < 8
   3. Cx = 8
   4. Dx > 8

   How do you know?
4. 4

   Warm restartSolve: x + 10 ≥ 25

   1. Ax ≥ 35
   2. Bx ≥ 15
   3. Cx ≤ 15
   4. Dx = 15

   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 throughSolve 320 + r ≤ 500.

   1. Ar ≤ 180
   2. Br ≤ 820
   3. Cr ≥ 180
   4. Dr ≤ 500

   Why is that the answer?
2. 6

   Think it throughSolve 4f = 60.

   1. Af = 15
   2. Bf = 240
   3. Cf = 64
   4. Df = 56

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

   Think it throughWhy is one an equation and the other an inequality?

   1. AThe flashlights cost exactly $60, but the budget is a limit she must stay under
   2. BBecause equations are for money and inequalities are for counting
   3. CBecause 4 is smaller than 320
   4. DThere is no real difference

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

   Back to the modelHow do you decide whether a word problem needs an equation or an inequality?

Use the words

Fill each blank with a word from the bank.

• Use an equation for one exact value and an ___ for a range.
• A drawing, equation, or diagram that represents a situation is a ___.
• A math sentence with an equal sign is an ___.
• A math sentence that compares values with <, >, ≤, or ≥ is an ___.

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 Equations and Inequalities Problem Solving is matching the wrong model to a key phrase.
2. 10

   Say moreWhat was your plan to solve this problem, and how did you check that your answer was reasonable?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Detective Chen is comparing two case notes. Note A says: 'The evidence locker holds exactly 54 files, split equally among 6 shelves.' Note B says: 'The surveillance van must stay parked for no more than 45 minutes.'

   Show your work

Last check

These two come from Lesson 8.6. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A box of donuts has some donuts. After giving away 7, there are fewer than 5 left. Which inequality represents the starting number of donuts d?

   1. Ad − 7 < 5
   2. Bd + 7 < 5
   3. Cd − 7 > 5
   4. Dd − 7 = 5

   Explain your choice.
2. 13

   From Lesson 8.6Explain your thinking — Solve and describe the graph: x + 5 < 11

   1. Ax < 6; open circle at 6, shade left
   2. Bx < 16; open circle at 16, shade left
   3. Cx ≤ 6; closed circle at 6, shade left
   4. Dx > 6; open circle at 6, shade right

   How do you know?
3. 14

   From Lesson 8.6How is s ≥ 27 graphed?

   1. AClosed circle at 27, shaded to the right
   2. BOpen circle at 27, shaded to the right
   3. CClosed circle at 27, shaded to the left
   4. DOpen circle at 27, shaded to the left

   How do you know?

Be honest — this tells your teacher what to do next