Start here

Use the model to solve the first problem. Then try these quick review questions from earlier lessons.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step. 🔊 Listen 💡 Hint

   Try it together — then prove it:

   1. Solve x − 5 ≤ 8. Then graph the solution and explain the symbol.
   2. Add 5 to both sides. What do you get? (x ≤ 8 + 5, so x ≤ 13.)
   3. Which circle do we draw? Which way do we shade? (A closed circle at 13. Shade left.)
   4. Put 10 in for x. Is it true? (Yes. 10 − 5 = 5, and 5 ≤ 8.)
   5. Why does the ≤ symbol stay the same after adding 5? (Adding the same amount to both sides moves both by the same amount. The smaller side stays smaller.)

   Show your work
2. 2

   Quick reviewWhich graph represents x > 8? 🔊 Listen 💡 Hint

   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

   Quick reviewWhich graph represents x ≤ 10? 🔊 Listen 💡 Hint

   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

   Quick reviewWhich graph represents x < 5? 🔊 Listen 💡 Hint

   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?

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughSolve 48 + s ≥ 75. 🔊 Listen 💡 Hint

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

   Why is that the answer?
2. 6

   Think it throughIs exactly $27 enough? 🔊 Listen 💡 Hint

   1. ANo — she needs more than 27
   2. BYes — 'at least' includes 27 exactly
   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? 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

Use the words

Fill each blank with a word from the bank.

• 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 ___.
• To check a solution, I ___ the value back into the inequality.

Explain the thinking

1. 9

   Find the mistakeRead the mistake. Explain what went wrong, then show the correct step. 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint
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. 🔊 Listen 💡 Hint

   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 🔊 Listen 💡 Hint

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

   Explain your choice.
2. 13

   From Lesson 8.5Explain your thinking — How would you graph the inequality x ≥ 9? 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

   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

   How do you know?

Check your progress

Choose the box that best describes how you feel about each skill.