Section Exercises
1. When solving an inequality, explain what happened from Step 1 to Step 2:
2. When solving an inequality, we arrive at
Explain what our solution set is.
3. When writing our solution in interval notation, how do we represent all the real numbers?
4. When solving an inequality, we arrive at
Explain what our solution set is.
5. Describe how to graph
For the following exercises, solve the inequality. Write your final answer in interval notation.
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For the following exercises, solve the inequality involving absolute value. Write your final answer in interval notation.
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For the following exercises, describe all the x-values within or including a distance of the given values.
24. Distance of 5 units from the number 7
25. Distance of 3 units from the number 9
26. Distance of 10 units from the number 4
27. Distance of 11 units from the number 1
For the following exercises, solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation.
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For the following exercises, graph the function. Observe the points of intersection and shade the x-axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation.
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For the following exercises, graph both straight lines (left-hand side being y1 and right-hand side being y2) on the same axes. Find the point of intersection and solve the inequality by observing where it is true comparing the y-values of the lines.
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For the following exercises, write the set in interval notation.
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For the following exercises, write the interval in set-builder notation.
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For the following exercises, write the set of numbers represented on the number line in interval notation.
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![A number line with two tick marks labeled: -2 and 1 respectively. There is an open circle around the -2 and a dot on the 1 with an arrow connecting the two.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/09/25200423/CNX_CAT_Figure_02_07_211.jpg)
![Number line with two tick marks labeled: -1 and 2 respectively. There is an open circle around the tick mark labeled -1 and a line that extends leftward from the circle. There is a dot around the tick mark labeled 2 and a line that extends rightward from the dot.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/09/25200424/CNX_CAT_Figure_02_07_212.jpg)
![Number line with one tick mark labeled 4. There is a dot on the tick mark and an arrow extending leftward from the dot.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/09/25200426/CNX_CAT_Figure_02_07_213.jpg)