Question

Solve | x + 6| - 7 = 8

A: x= -9 and x = -21

B: x = 9 and x = -9

C: x = -9 and x = 21

D: x = 9 and x = -21
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Answer 1

x = 9,-21

Explanation:

Given:

`\displaystyle \largex+6`

Transport -7 to add 8:

`\displaystyle \large=8+7\\\displaystyle \largex+6`

Cancel absolute sign and add plus-minus to 15:

`\displaystyle \large{x+6=\pm 15}`

Transport 6 to subtract ±15:

`\displaystyle \large{x=\pm 15-6}`

Consider:

`\displaystyle \large{x= 15-6}` or
`\displaystyle \large{x = -15-6}`

`\displaystyle \large{x=9}` or
`\displaystyle \large{x=-21}`

Solution:

`\displaystyle \large{x = 9}` or
`\displaystyle \large{x=-21}`

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Second Method

Given:

`\displaystyle \large`

Transport -7 to add 8:

`\displaystyle \large=8+7\\\displaystyle \largex+6`

Absolute Function Property:

`\displaystyle \large{|x-a| = \begin{cases} x-a \ \ (x \geq a) \\ -x+a \ \ (x < a) \end{cases}}`

Consider both intervals:

When x ≥ a then:

`\displaystyle \large\\\displaystyle \large{x+6=15}`

Transport 6 to subtract 15:

`\displaystyle \large{x=15-6}\\\displaystyle \large{x=9}`

When x < a then:

`\displaystyle \large=15\\\displaystyle \large{-(x+6)=15}\\\displaystyle \large{-x-6=15}`

Transport -6 to add 15:

`\displaystyle \large{-x=15+6}\\\displaystyle \large{-x=21}`

Transport negative sign to 21:

`\displaystyle \large{x=-21}`

Solution:

`\displaystyle \large{x=9}` or
`\displaystyle \large{x=-21}`

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