Find all real solutions of the equation. $| 7 x + 1 | = 7$
A) $x = - 8$ ,
$x = 8$
B) $x = - \frac { 8 } { 7 }$ ,
$x = \frac { 6 } { 7 }$
C) $x = - \frac {8 } { 7 }$ ,
$x = - 1$
D) $x = - \frac { 7 } { 8 }$ ,
$x = \frac { 7 } { 6 }$
E) no solution

Question

Quizplus · Accepted Answer

We can break the given equation into two cases:

Case 1: $7x+1=7$
Solving for $x$, we get $x=\frac{6}{7}$.

Case 2: $7x+1=-7$
Solving for $x$, we get $x=-\frac{8}{7}$.

Therefore, the solutions are $x=\frac{6}{7}$ and $x=-\frac{8}{7}$, which is given in choice B.

Find All Real Solutions of the Equation ∣7x+1∣=7| 7 x + 1 | = 7∣7x+1∣=7

Find All Real Solutions of the Equation $| 7 x + 1 | = 7$