Question

7 + | x - 8 | = 6

Answer 1

x=7

Answer 2

\(\bf 7 + | x - 8 | = 6\implies | x - 8 | =6-7\implies | x - 8 | =-1\\ \quad \\
| x - 8 | =-1\implies
\begin{cases}
+(x - 8 ) =-1\implies x-8=-1\\ \quad \\
\bf -(x - 8 ) =-1\implies x-8=1
\end{cases}\)

Answer 3

so x= -1 and x=1

Answer 4

well, if you add +8 to both sides, you'd end up with \(\bf | x - 8 | =-1\implies
\begin{cases}
+(x - 8 ) =-1\implies x-8=-1\implies x=8-1\\ \quad \\
\bf -(x - 8 ) =-1\implies x-8=1\implies x=8+1
\end{cases}\)

Answer 5

so x= no solution

Answer 6

well.... notice above, you do have 2 solutions

Answer 7

\({\bf | x - 8 | =-1\implies}
\begin{cases}
+(x - 8 ) =-1\implies x-8=-1\implies \color{blue}{x=8-1}\\ \quad \\
-(x - 8 ) =-1\implies x-8=1\implies \color{blue}{x=8+1}
\end{cases}\)

Answer 8

What a mugu!