How do you solve #6abs(2x-4)=54#?

Question

Eva Abramson · Accepted Answer

Divide both sides by #6#. Clear the absolute value sign by splitting the equation into two parts, one positive and one negative. Solve each for #x#.

#6abs(2x-4)=54# Divide both sides by #6#. #abs(2x-4)=9# Clear the absolute value sign by splitting the equation into two parts, one positive and one negative. #(2x-4)=9# and #-(2x-4)=9# Positive Equation #(2x-4)=9# Add 4 to both sides. #2x=9+4=13# Divide both sides by #2#. #x=13/2# Negative Equation #-(2x-4)=9# = #-2x+4=9# Subtract 4 from both sides. #-2x=9-4=5# Divide both sides by -2. #x=-5/2# #x=-5/2, 13/2#

Isaiah Anthony · Answer

undefined To solve the equation $6|2x - 4| = 54$, follow these steps:

1. Divide both sides by 6 to isolate the absolute value term: $\frac{6|2x - 4|}{6} = \frac{54}{6}$.

2. Simplify both sides: $|2x - 4| = 9$.

3. Set up two equations: $2x - 4 = 9$ and $2x - 4 = -9$.

4. Solve each equation separately:
   a) For $2x - 4 = 9$, add 4 to both sides, then divide by 2: $2x = 13$, $x = \frac{13}{2}$.
   b) For $2x - 4 = -9$, add 4 to both sides, then divide by 2: $2x = -5$, $x = -\frac{5}{2}$.

Therefore, the solutions are $x = \frac{13}{2}$ and $x = -\frac{5}{2}$.