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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
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.
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.
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