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Which statement is true about the solution(s) of I2x −13I = 9?A There is one...

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zoeeyz | Student, College Freshman | eNoter

Posted July 1, 2012 at 3:04 PM via web

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Which statement is true about the solution(s) of I2x −13I = 9?

A There is one solution, it is negative.

B There are two solutions, both positive.

C There are two solutions, one positive and one negative.

D There is one solution, it is positive.

E There are two solutions, both negative.

2 Answers | Add Yours

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 1, 2012 at 3:28 PM (Answer #1)

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You should solve the equation using absolute value properties such that:

`2x - 13 = 9 and 2x - 13 = -9`

Solving for x the equation `2x - 13 = 9 ` yields:

`2x - 13 = 9 =gt 2x = 13 + 9 =gt 2x = 22 =gt x = 11`

Solving for x the equation `2x - 13 = -9`  yields:

`2x - 13 = -9 =gt 2x = 13 - 9 =gt 2x = 4 =gt x = 2` 

Hence, evaluating the solutions to equation `|2x - 13| = 9`  yields two positive solutions, thus, you need to select the B option.

Sources:

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mjripalda | High School Teacher | (Level 3) Educator

Posted July 1, 2012 at 3:36 PM (Answer #2)

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Take note that in absolute value equations there are two cases.

I.    Z > 0   

II.  Z  < 0 

where Z represent the expression inside the absolute value.

Use these two cases to determine the solution.

|2x −13| = 9

Case I:   Z > 0                             Case II: Z < 0

       2x - 13 = 9                                      - (2x - 13) = 9

              2x = 9 + 13                                 -2x + 13 = 9 

              2x = 22                                              - 2x = 9 - 13

                x = 11                                              -2x  = -4  

                                                                           x  = 2 

Answer: B There are two solutions, both positive.

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