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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: Graph x < 5 on a number line. What number is the boundary? (5) Is 5 included? Which circle do we use? (No. Use an open circle at 5.) Which way do we shade for "less than"? (Left, toward smaller numbers.) Test x = 3. Is 3 < 5 true? (Yes. 3 is in the shaded part.)

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

   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
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
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

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?

   I chose ___ because ___ .
2. 6

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

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

   How do you know?

   I chose ___ because ___ .
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.

   I chose ___ because ___ .
4. 8

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

   I use a ___ circle when the symbol is ___ because the boundary value ___ part of the solution.

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?

   I used a ___ circle because the symbol ___ means the boundary is ___.
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 8.4. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowQuick check — you've got this: 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.

   I know it is ___ because ___ .
2. 13

   From Lesson 8.4Quick 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
3. 14

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

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

Be honest — this tells your teacher what to do next