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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: Solve x − 5 ≤ 8. What is the inverse of subtracting 5? We add 5 to both sides: x ≤ 8 + 5, so x ≤ 13. ≤ includes 13, so we use a closed circle and shade left. Substitute x = 10: 10 − 5 = 5 ≤ 8. True? Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartWhich graph represents x > 8?

   1. AClosed circle at 8, shaded right
   2. BOpen circle at 8, shaded right
   3. COpen circle at 8, shaded left
   4. DClosed circle at 8, shaded left

   How do you know?
3. 3

   Warm restartWhich graph represents x ≤ 10?

   1. AOpen circle at 10, shaded left
   2. BClosed circle at 10, shaded left
   3. CClosed circle at 10, shaded right
   4. DOpen circle at 10, shaded right

   How do you know?
4. 4

   Warm restartWhich graph represents x < 5?

   1. AClosed circle at 5, shaded left
   2. BOpen circle at 5, shaded right
   3. COpen circle at 5, shaded left
   4. DClosed circle at 5, shaded right

   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 48 + s ≥ 75.

   1. As ≥ 27
   2. Bs ≥ 123
   3. Cs ≤ 27
   4. Ds ≥ 75

   Why is that the answer?
2. 6

   Think it throughIs exactly $27 enough?

   1. AYes — 'at least' includes 27 exactly
   2. BNo — she needs more than 27
   3. CNo — she needs 75
   4. DOnly if she saves more

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

   Think it throughHow 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

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

   Back to the modelHow is solving an inequality similar to and different from solving an equation?

Use the words

Fill each blank with a word from the bank.

• Isolate the variable first, then show the whole ___ ___ on a number line.
• To find all the values that make an inequality true is to ___ it.
• To show the solutions on a number line is to ___ them.
• A value that makes an inequality true is a ___.

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 Solve and Graph Inequalities is shading the number line in the wrong direction after solving.
2. 10

   Say moreWhat steps did you follow to solve and then graph the inequality, and how did you check a value to make sure your solution set is right?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Detective Ortiz is reviewing a stakeout log. The team's rule is that a suspect's vehicle must be parked for more than 20 minutes before they radio for backup. The log lists parked times of 15, 20, and 25 minutes.

   Show your work

Last check

These two come from Lesson 8.5. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain 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

   Explain your choice.
2. 13

   From Lesson 8.5Explain 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

   How do you know?
3. 14

   From Lesson 8.5How would the graph change if 12 or fewer people were at the scene?

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

   How do you know?

Be honest — this tells your teacher what to do next