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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.

   Try it together — then prove it: Graph x < 5 on a number line. Then explain the circle. What is the boundary? Which circle do we use? (5. Use an open circle.) Which way do we shade? (Left, toward smaller numbers.) Why is the circle at 5 open, not closed? (5 < 5 is false. So 5 is not a solution, and the circle stays empty.)

   Show your work
2. 2

   Warm restartWhich inequality represents: 'You must be at least 48 inches tall to ride'?

   1. Ah > 48
   2. Bh ≥ 48
   3. Ch < 48
   4. Dh ≤ 48

   How do you know?
3. 3

   Warm restartWhich inequality represents: 'A store can hold no more than 75 people'?

   1. Ap < 75
   2. Bp ≥ 75
   3. Cp ≤ 75
   4. Dp > 75

   How do you know?
4. 4

   Warm restartWhich inequality represents: 'The speed limit is more than 25 mph'?

   1. As ≥ 25
   2. Bs < 25
   3. Cs > 25
   4. Ds = 25

   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 throughWhy did the detective use an open circle at 12?

   1. ABecause 12 is negative
   2. BBecause the shading goes left
   3. CBecause 12 is not a whole number
   4. DBecause p < 12 does not include 12 itself

   Why is that the answer?
2. 6

   Think it throughWhich number is a solution to p < 12?

   1. A11
   2. B12
   3. C13
   4. D15

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

   Think it throughHow would the graph change if 12 or fewer people were at the scene?

   1. AThe shading would flip to the right
   2. BNothing would change
   3. CThe circle would be closed (filled in) at 12
   4. DThe circle would move to 11

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

   Back to the modelHow do you decide between an open circle and a closed circle when graphing?

Use the words

Fill each blank with a word from the bank.

• A line with numbers in order used to show values and solutions is a ___.
• A hollow circle that shows a value is NOT included, used for < or >, is an ___.
• A filled-in circle that shows a value IS included, used for ≤ or ≥, is a ___.
• All the values that make an inequality true form the ___.

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 Graph Inequalities is treating ≥ and ≤ the same as > and < and drawing the wrong circle.
2. 10

   Say moreWhen you graphed x > 4 and x ≤ 7, why did you use an open circle on one and a closed circle on the other?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Four number lines are shown, and every one of them is marked at 5. Two use an open circle and two use a filled-in circle, and the shading runs a different direction on each line.

   Show your work

Last check

These two come from Lesson 8.4. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — How would you graph the inequality x ≥ 9?

   1. AClosed circle at 9, shaded right
   2. BOpen circle at 9, shaded right
   3. CClosed circle at 9, shaded left
   4. DOpen circle at 9, shaded left

   Explain your choice.
2. 13

   From Lesson 8.4Explain your thinking — Which inequality represents: 'A number n is at least 14'?

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

   How do you know?
3. 14

   From Lesson 8.4Which inequality means 'at most 65'?

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

   How do you know?

Be honest — this tells your teacher what to do next