Solve the equation. $| 6 - 5 x | - 6 = 15$
A) $x = - 3$
B) $x = \frac { 27 } { 5 } , - 3$
C) $x = \frac { 27 } { 5 }$
D) $x = 3 , - 3$
E) no solution

Question

Quizplus · Accepted Answer

First, we isolate the absolute value by adding 6 to both sides:
$$|6-5x|=21$$
Now we have two cases to consider:
Case 1: $6-5x \geq 0$
If $6-5x \geq 0$, then $|6-5x|=6-5x$ so we have:
$$6-5x=21$$
Solving for $x$, we get $x=-\frac{27}{5}$. 
However, we need to check if this solution satisfies the initial assumption that $6-5x\geq0.$
$$6-5\cdot\left(-\frac{27}{5}\right) = 6 + 27 =33>0$$
Therefore, $x=-\frac{27}{5}$ is a valid solution. 
Case 2: $6-5x<0$
If $6-5x<0$, then $|6-5x|=-(6-5x)=5x-6$ so we have:
$$5x-6=21$$
Solving for $x$, we get $x=\frac{27}{5}$.
However, we need to check if this solution satisfies the initial assumption that $6-5x<0.$
$$6-5\cdot\left(\frac{27}{5}\right) = 6 - 27 =-21<0$$
Therefore, $x=\frac{27}{5}$ is not a valid solution.
Overall, we have two solutions: $x=-\frac{27}{5}$ (from Case 1) and $x=-3$ (obtained from either case by plugging in the value for $|6-5x|$). Therefore, the answer is choice B.

Solve the Equation ∣6−5x∣−6=15| 6 - 5 x | - 6 = 15∣6−5x∣−6=15

Solve the Equation $| 6 - 5 x | - 6 = 15$