# 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...

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.

Posted on

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.

Posted on

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: