Question

2/3 (w+12) = 3w-6
Solution, no solution, or infinite solutions

Answer 1

This would be no solutions
2/3(w+12)=3w-6
Multiply what’s inside the parentheses by 2/3
2/3w+8=3w-6
Move the 3w and -6 to the other side
-3 and 2/3w+2=0
Make -3 and 2/3 an improper fraction
-11/3w+2=0
Move the 2 over
-11/3w=-2
Divide the sides by 3
-11/3 divide by 3 = -2/3
Which gives us
-1.22222222223= -2/3
The 2/3 is a negative -2/3
Therefore it’s no solution

Answer 2

w = 6

Explanation:

`(2)/(3)(w+12)=3w-6\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup\cdot(2)/(3\!\!\!\!\diagup)(w+12)=(3)(3w)-(3)(6)\\\\2(w+12)=9w-18\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(2)(w)+(2)(12)=9w-18\\\\2w+24=9w-18\qquad\text{subtract 24 from both sides}\\\\2w+24-24=9w-18-24\\\\2w=9w-42\qquad\text{subtract}\ 9w\ \text{from both sides}\\\\2w-9w=9w-9w-42\\\\-7w=-42\qquad\text{divide both sides by (-7)}\\\\(-7w)/(-7)=(-42)/(-7)\\\\w=6`