Objective: Section 1.7 Solving Absolute Value Equations and Inequalities

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5 Minute Check

Solve and graph the following.

1.

2.

3. -3t – 5 < -8 or -4t + 3 > 7

243

2p

3523 x

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What you will learn today

How to solve an absolute value equation How to solve an absolute value

inequality How to graph the solution to an absolute

value inequality

Objective: Section 1.7 Solving Absolute Value Equations and Inequalities

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Absolute Value Equations and Inequalities

The absolute value of a number x, written |x|, is the distance the number is from zero on the number line. The absolute value of a number is always positive (distance is always positive).

Objective: Section 1.7 Solving Absolute Value Equations and Inequalities

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Question? What are the possible values for x?

|x| = 5

Objective: Section 1.7 Solving Absolute Value Equations and Inequalities

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Question? What are the possible values for x?

|x| = 5

Which leads to the following “rule”.The absolute value

equation |ax+b|=c, where c > 0, is equivalent to the compound statement ax + b = c or ax + b = -c.

Objective: Section 1.7 Solving Absolute Value Equations and Inequalities

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Solving an Absolute Value Equation Solve |2x – 5| = 9

Objective: Section 1.7 Solving Absolute Value Equations and Inequalities

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You Try Solve |2 – 4x| = 10

Objective: Section 1.7 Solving Absolute Value Equations and Inequalities

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Inequality Rules The inequality |ax + b| < c, where c > 0,

means that ax + b is between –c and c. This is a compound “and” inequality. It is equivalent to –c<ax + b<c

The inequality |ax + b| > c, where c > 0, means that ax + b is beyond –c and c. This is an “or” compound inequality. It is equivalent to ax + b < -c or ax + b > c.

Objective: Section 1.7 Solving Absolute Value Equations and Inequalities

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Solving an Absolute Value InequalitySolve: |2x + 7| < 11

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

Objective: Section 1.7 Solving Absolute Value Equations and Inequalities

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You Try Solve 21|94| x

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

Objective: Section 1.7 Solving Absolute Value Equations and Inequalities

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Another Example Solve 8|23| x

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

Objective: Section 1.7 Solving Absolute Value Equations and Inequalities

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You Try Solve: |-3x + 10| > 7

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

Objective: Section 1.7 Solving Absolute Value Equations and Inequalities

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A Question What is wrong with the following?

|3x – 5| < -10

Objective: Section 1.7 Solving Absolute Value Equations and Inequalities

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An Application A cereal manufacturer has a tolerance of

.75 ounce for a box of cereal that is supposed to weigh 20 ounces. Write and solve an absolute value inequality that describes the acceptable weights for 20 ounce boxes.

Objective: Section 1.7 Solving Absolute Value Equations and Inequalities

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Homework Page 53, problems 32-36 even, 42-46

even, 48, 50, 54, 68