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Practice 1: Solve : | x +4| = -6

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Practice 2: Solve : | 2x +4| = x - 5 Answer: ____,____

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**An absolute value equation has 3 parts:**

A variable A middle value (mean) A distance from the middle to the either end (must be the same) The equation you use is | variable – mean | = distance One possible question is that you are given the two answers for example the solutions are 7 and -7: To write and absolute value from this you need to find the middle(average of these two answers) divided by 2 = 0 So 0 is your mean. Now you need to find out how far it is from the middle to the end(answer). 7 – 0 = 7. This one was easy because the middle was 0. The equation you use is | x –0 | = 7 or |x| = 7

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Example 1: Write an absolute value equation that has -1 and 11 as solutions. To write and absolute value from this you need to find the middle(average of these two answers) divided by 2 = 5 So 5 is your mean. Now you need to find out how far it is from the middle to the end(answer). 11 – 5 = 6. The equation you use is | variable – mean | = distance The equation is: | x – 5 | = 6

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Practice 3: Write an absolute value equation that has the solutions -2 and 3.

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**| x – 47 | = 1.5 EXAMPLE 2 Solve an inequality of the form |x + b| = c**

A factory produces widgets whose length must be within 1.5 mm of an ideal length of 47mm. A factory supervisor wants to mark a rulers with the least and greatest acceptable length for each widget for workers to use in quality control let x be the length of the markings. SOLUTION Write a verbal model. Then write an inequality. STEP 1 |Actual length (the variable) Ideal length| (the middle or mean) = the variance (How far the mean is from the outer most possibility) | x – 47 | = 1.5

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Practice 4 You and your friends Jose and Sarah all live on the same street. You know that Jose lives 5 blocks away from you. Jose says that Sarah lives two blocks from him, but he didn’t say whether she lives closer to you the he does or Further. Let b be the number of blocks Sarah might live from you. Set up What is the middle or mean of this problem? What is the variance or change? Use these to set up and absolute value equation.

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EXAMPLE 1 Using Mental Math to Solve Equations a. 15 – n = 4 b. 8x = 32 c.r 12 = 4 Solve the equation using mental math.

EXAMPLE 1 Using Mental Math to Solve Equations a. 15 – n = 4 b. 8x = 32 c.r 12 = 4 Solve the equation using mental math.

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