Solve the equation.
$| 7 x + 12 | = | x - 6 |$
A) $x = - 3$
B) $x = - \frac { 3 } { 4 } , x = - 3$
C) $x = - \frac { 5 } { 6 } , x = 4$
D) $x = - \frac { 5 } { 6 } , x = - 3$
E) no solution

Question

Solve the equation. 
$| 7 x + 12 | = | x - 6 |$
A) $x = - 3$
B) $x = - \frac { 3 } { 4 } , x = - 3$
C) $x = - \frac { 5 } { 6 } , x = 4$
D) $x = - \frac { 5 } { 6 } , x = - 3$
E) no solution

Quizplus · Accepted Answer

To solve $| 7x + 12 | = | x - 6 |$, we consider two cases due to the absolute value:1. $7x + 12 = x - 6$Solving for $x$, we subtract $x$ from both sides and subtract $12$ from both sides:$6x = -18$$x = -3$2. $7x + 12 = -(x - 6)$Expanding and solving for $x$, we get:$7x + 12 = -x + 6$$8x = -6$$x = -\frac{3}{4}$Thus, the solutions are $x = -3$ and $x = -\frac{3}{4}$, which corresponds to choice B.

Solve the Equation ∣7x+12∣=∣x−6∣| 7 x + 12 | = | x - 6 |∣7x+12∣=∣x−6∣

Solve the Equation $| 7 x + 12 | = | x - 6 |$