Solve: $| 7 x - 4 | = | x - 5 |$
A) $\left\{ - \frac { 1 } { 6 } \right\}$
B) $\left\{ - \frac { 1 } { 8 } , - \frac { 1 } { 6 } \right\}$
C) $\left\{ - \frac { 1 } { 6 } , \frac { 9 } { 8 } \right\}$
D) $\left\{ \frac { 1 } { 6 } , \frac { 9 } { 8 } \right\}$

Question

Quizplus · Accepted Answer

The given equation can be rewritten as two separate equations:
\begin{align*}
7x-4 &= x-5 \quad \Rightarrow \quad x = \frac{9}{6} = \frac{3}{2}\
7x-4 &= -(x-5) \quad \Rightarrow \quad x = -\frac{1}{6}
\end{align*}
Therefore, the solutions are $-\frac16$ and $\frac98$, which are given in choice C.

Solve ∣7x−4∣=∣x−5∣| 7 x - 4 | = | x - 5 |∣7x−4∣=∣x−5∣

Solve $| 7 x - 4 | = | x - 5 |$