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Published byGyles Hunt Modified over 8 years ago

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**4-6 Solving Absolute Value Equations & Inequalities**

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**Absolute Value (of x) Symbol**

Represents the distance x is from zero on the number line. Always positive Ex:

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**So there are two answers!**

Ex: What are the possible values of x? x = or x = -5 So there are two answers!

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**Solving an absolute value equation:**

ax+b = c, where c>0 This problem will also have two answers! Set up 2 new equations, then solve. ax+b = c and ax+b = -c

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**NB: Make sure the absolute value is by itself before you split to solve**

If the absolute value isn’t by itself, solve until it is. Ex. Don’t set up 2 new equations until the absolute value is by itself! isn’t the same as

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**Ex: To solve set up two equations…**

6x-3 = or 6x-3 = -15 Add 3 to both sides: 6x = or 6x = -12 Divide both sides by 6 x = 3 or x = -2 * Plug in answers to check your solutions!

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**Get the absolute value part by itself by adding 3 to both sides!**

Ex: To solve Get the absolute value part by itself by adding 3 to both sides! Now split into 2 parts. 2x+7 = 11 or 2x+7 = -11 Add (-7) to both sides 2x = 4 or 2x = -18 Divide both sides by 2 x = 2 or x = -9 Check the solutions.

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**Absolute Value Inequalities!**

You can also solve: Absolute Value Inequalities!

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**The method for solving Absolute Value Inequalities depends on the inequality symbol.**

Think about what this means…what values for x make this statement true? Let’s plot them on a number line. If it’s a less than problem, change it into an “and” compound inequality. means AND Another way to write this is…..

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**The method for solving Absolute Value Inequalities depends on the inequality symbol.**

If it’s a less than problem, change it into an “and” compound inequality. To write it algebraically:

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**The method for solving Absolute Value Inequalities depends on the inequality symbol.**

If it’s a greater than problem, change it into an “or” compound inequality. Think about what this means…what values for x make this statement true? Let’s plot them on a number line. If it’s a greater than problem, change it into an “or” compound inequality. means OR

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**The method for solving Absolute Value Inequalities depends on the inequality symbol.**

If it’s a greater than problem, change it into an “or” compound inequality. OR To write it algebraically: Becomes an “or” problem Change to: ax+b > c or ax+b < -c

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**Solve & graph. Less than means it becomes an “and” problem * Add 3**

* Divide by 2

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**Solve & graph. Add -3 Add 2 Divide by 2**

Get absolute value by itself first. Add -3 Since it’s greater than, it becomes an “or” problem Add 2 Divide by 2

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