Solve $\left| \frac { 4 z + 5 } { 6 } \right| - 2 = 6$ , if possible.
A) $z = 43$ , $z = - 53$
B) $z = - \frac { 43 } { 4 }$ , $z = - \frac { 53 } { 4 }$
C) $z = \frac { 43 } { 4 }$ , $z = - \frac { 53 } { 4 }$
D) $z = \frac { 43 } { 4 }$ , $z = \frac { 53 } { 4 }$
E)no solution

Question

Quizplus · Accepted Answer

First, solve the equation $\left| \frac { 4 z + 5 } { 6 } \right| = 8$. This gives two cases: $\frac { 4 z + 5 } { 6 } = 8$ and $\frac { 4 z + 5 } { 6 } = -8$. Solving these, we get $z = \frac {43}{4}$ and $z = -\frac{53}{4}$.

Solve ∣4z+56∣−2=6\left| \frac { 4 z + 5 } { 6 } \right| - 2 = 6​64z+5​​−2=6

Solve $\left| \frac { 4 z + 5 } { 6 } \right| - 2 = 6$