Inequalities Determine whether each number is a solution of the given inequality. Graphing Inequalities Solving Inequalities Solving Multi-Step Inequalities Compound Inequalities Absolute Value Inequalities Graph each inequality. Write an inequality for each graph. m < 1 A car dealership sells at least 35 cars each week. Define a variable and write

an inequality for each situation. 2(m + 1) < –6 a. –6 b. –4 c. –2 n ≥ 5 j > –4 k ≤ 10 No more than 425 tickets to a musical will be sold. You must be at least

18 years old to vote. The party store sold more than 720 balloons in July. A solution of an inequality is any number that makes the inequality true. A family earns at most $2500 a month. The family’s monthly expenses are $2000. Write and solve an inequality to find the possible amounts of money the family could save each month. A local television station sponsors a food drive. The goal is to donate more than 1000 canned goods. The station already has collected 400 canned goods. How many more canned goods does the television station need to meet its goal? Write and solve an inequality to find the number of canned goods needed. A company sells parts in both the United States and in Europe. The company must report its product’s size in both the metric system and in inches. If a product is reported to be no more than 12 inches long, how long is it in centimeters? Assume 1 inch = 2.54 cm. You want to see if you are really saving money each month by exclusively using your cell phone for all long distance calls. Long distance calls cost $.03 per minute on your cell phone. The basic plan for your cell phone is $30 each month. The cost of regular phone service with unlimited long distance is $40. Write and solve an inequality to find the number of long-distance call minutes you may make and still save money. 9 + p ≤ 17 –8w < 24 t – 5 ≥ –13 9h > –108 You can solve inequalities using multiplication or division using these two important rules.

•You can multiply or divide each side of an inequality by a positive number.

•You can multiply or divide each side of an inequality by a negative number only if you reverse the inequality sign. 6 – 3k > 45 6(n – 3) + 4n ≤ 42 7p + 12 > 6p – 15 8(2f + 3) + 4f ≤ –16 A student had $45 when she went to the mall. She spent $9 on a pair of earrings. Then she wants to buy some CDs that cost $12 each. Write and solve an inequality to determine how many CDs she can buy. A friend needs at least $125 to go on the class trip. He has saved $45. He makes $20 for each lawn he mows. Write and solve an inequality to determine how many lawns he needs to mow to go on the trip. 17 ≤ 2x + 7 ≤ 29 3t – 5 < –8 or 2t + 5 > 17 h – 7 ≥ –5 h + 4 < 10 –4 ≤ 4d + 24 ≤ 4 5m – 2 < 8 or 6m – 2 > 6 + 5m Interval Notation Use (or) when a < or > symbol indicates that the interval's endpoints are not included.

Use [ or ] when a ≤ or ≥ symbol indicates that the interval's endpoints are included.

Use ∞ when the interval continues forever in a positive direction.

Use –∞ when the interval continues forever in a negative direction. Parentheses:

Brackets:

Infinity: [0, ∞) (–2, 3] [–4, ∞) 4 = |x| – 3 7 = |j| + 2 |a| > 2 |y – 4| > 8 | –6m + 2 | > 20 |3c| – 1 ≥ 11 |2b + 3| < 7 To solve an equation in the form |A| = b, where A represents a variable expression and b > 0, solve A = b and A = – b. Solving Absolute Values Equations

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# Solving Inequalities

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