Answer:
A
Step-by-step explanation:
Our equation is:
[tex]\frac{2}{3} *(\frac{1}{2} x+12)=\frac{1}{2} *(\frac{1}{3} x+14)-3[/tex]
Let's first distribute the left side. When distributing, we essentially find the sum of the product of the outside term with each of the inside terms. Here, the outside term is 2/3 and the inside terms are 1/2x and 12. So:
[tex]\frac{2}{3} *(\frac{1}{2} x+12)=\frac{2}{3} *\frac{1}{2} x+\frac{2}{3} *12=\frac{1}{3} x+8[/tex]
Now distribute the right side. Here, the outside term is 1/2 and the inside terms are 1/3x and 14, so:
[tex]\frac{1}{2} *(\frac{1}{3} x+14)-3[/tex]
[tex]\frac{1}{2} *(\frac{1}{3} x+14)-3=\frac{1}{2} *\frac{1}{3} x+\frac{1}{2} *14-3=\frac{1}{6} x+7-3=\frac{1}{6} x+4[/tex]
We now have:
[tex]\frac{1}{3} x+8=\frac{1}{6} x+4[/tex]
Isolate the variable by bringing 1/6x to the left and bringing 8 to the right:
[tex]\frac{1}{3} x-\frac{1}{6} x=4-8[/tex]
[tex]\frac{2}{6} x-\frac{1}{6} x=-4[/tex]
[tex]\frac{1}{6} x=-4[/tex]
x = -4 * 6 = -24
The answer is A.
