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.

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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:**

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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