Graphing Inequalities on a Number Line

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Show your work for each problem.

1.
What type of circle should you use for $x < 7$ ?
1. a)Closed circle (included)
2. b)Open circle (not included)
3. c)Either type works
4. d)No circle needed
2.
For $x \geq -3$ , which direction should you shade?
1. a)Right (toward larger numbers)
2. b)Left (toward smaller numbers)
3. c)Both directions
4. d)No shading needed
3.
For $x \leq 5$ , at which number do you place the circle?
4.
A graph shows a closed circle at $-2$ with shading to the right. Which inequality does it show?
1. a) $x > -2$
2. b) $x < -2$
3. c) $x \leq -2$
4. d) $x \geq -2$
5.
What is the largest integer that is a solution to $x < 4$ ?
6.
Which of these numbers is NOT a solution to $x > -5$ ?
1. a) $-7$
2. b) $10$
3. c) $-4$
4. d) $0$
7.
Write the inequality: open circle at 3, shading to the left. Use x and the correct symbol.
8.
Graph the inequality $x \leq -1$ step by step.
9.
The inequality $5 > x$ means the same as which of the following?
1. a) $x < 5$
2. b) $x > 5$
3. c) $x \geq 5$
4. d) $x \leq 5$
10.
Solve $x - 2 \geq 5$ and describe how to graph the solution.
11.
The graph shows an open circle at $-4$ with shading to the left. Write the inequality using x.
12.
Which value is a solution to $x \leq -6$ ?
1. a) $-4$
2. b) $-10$
3. c) $0$
4. d) $-5$
13.
A roller coaster requires riders to be at least 140 cm tall. Write and graph this as an inequality, using $h$ for height.
14.
Solve $2x < 10$ . What is the boundary point of the graph?
15.
For food safety, the temperature must stay below 8°C. Write the inequality using $t$ and describe the graph.
16.
A number line shows an open circle at 0 with shading to the right. Which statement is TRUE?
1. a)Zero is a solution
2. b)Negative numbers are solutions
3. c)All real numbers are solutions
4. d)All positive numbers are solutions