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| Introduction to Solving Inequalities |
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| In the following problems, solve each inequality. For inequality symbols that are non-keyboard entries, write the solutions as shown in the examples below. |
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| Hint: When you multiply or divide both sides of an inequality by a negative number, you must switch the direction of the arrow. |
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| 1) Solve the inequality. |
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| 3) Solve the inequality. |
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| For the next two problems, remember to apply the distributive property to BOTH terms inside parenthesis. |
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6) The Checkered Cab Company charges a flat rate of $1.75 flat rate in addition to $0.65 per mile. Mandy has no more than $12.00 to spend on a cab ride. Write an inequality to represent the situation. How many miles can Mandy travel without exceeding her limit?
(a) State the inequality, and then
(b) state the answer. Round the answer to the nearest mile.
Let x = number of miles
Think: Flat rate + Cost per mile is no more than $12 |
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| 7) Describe two kinds of compound inequalities. |
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| In the following problems, solve the compound inequalities. |
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12) Marcus has scores of 92, 87, 85 and 88 on four algebra tests. What score must he make on his exam to receive a “B” in the course, if the final exam counts as two tests? A “B” in the course is earned if the final average is between 83 and 91. Write a compound inequality to represent this situation.
Let x represent the test score, but remember that it counts as TWO test scores. |
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13) In the previous problem, what range of scores may Marcus receive to earn a “B” in the course.
Hint: Find the lowest score and find the highest score and then write an inequality or statement that covers all scores that could give him a "B". |
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| Solving Absolute Value Equations and Inequalities |
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| 14) True or False. The absolute value of a number is always positive. |
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In the following problems, solve the absolute value equations. Make sure to check all answers and look for extraneous roots.
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In the following problems, solve the absolute value inequalities.
Hint: To solve an absolute value inequality, write two inequalities and solve each inequality. |
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| In the following problems, select the graph that fits the solution to the given absolute value equation or the given absolute value inequality. |
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| 23) Choose the graph and phrase that fits the solution to this absolute value equation: |
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| 24) Choose the graph and phrase that fits the solution to this absolute value inequality: |
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| 25) Choose the graph and phrase that fits the solution to this absolute value inequality: |
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| 26) Choose the graph and phrase that fits the solution to this absolute value inequality: |
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| 27) Choose the graph and phrase that fits the solution to this absolute value equation: |
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| 33) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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| No offline activities found |
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