Question

Solve |x – 4| + 6 = 17.

A. X= 15 and x = -15
B. x= -15 and x= 7
C. x = 15 and x= -7
D. x = -15 and x = -7

Answer 1

`\mathrm{C)\:}x=15,\:-7`

Explanation:

For
`|a-b|=c`, there are two possible cases:

`\begin{cases}a-b=c\\a-b=-c\\\end{cases}`

Solving for both cases, we get:

`\begin{cases}x-4+6=17, \:x+2=17, \: \fbox{$x=15$}\\-(x-4)+6=17,\: -x+10=17, \: -x=7, \:, \fbox{$x=-7$}\\\end{cases}`