The subtraction of 2w on both sides leads to an inconsistency: -4 = 2w + 2. Recognizing this earlier, the equation is inconsistent, and there is no solution.
Start with the equation: (1/3)(6w-12) = 2w + 2
Distribute 1/3 to both terms inside the parentheses:
(2w - 4) = 2w + 2
Subtract 2w from both sides:
-4 = 2
At this point, you've reached the false statement -4 = 2, indicating an inconsistency. However, you could have identified this earlier in the process. Notice that in the original equation, both sides have a term with 2w. When you subtract 2w from both sides, you end up with -4 on the left side and 2 on the right side.
This inconsistency implies that, regardless of the value of w, the equation cannot be satisfied. Therefore, you could have stopped at the point where you subtracted 2w from both sides, recognizing that the equation is inconsistent:
-4 = 2w + 2
This simplifies to -4 = 2, and you can conclude that there is no solution without proceeding further.
Complete question:
How many solutions does 1/3 (6w-12)=2w+2 have? You can rewrite the equation until you identify a true statement like 3=3, identify a false statement like 1=4 , or solve for w. 1/3 (6w-12)=2w+2 2w-4=2w+2 -4=2 -4=2 is a false statement. No value of w makes the equation true. So the equation has no solution. 1 Could you have stopped solving the equation in the Example sooner, before you reached the false statement -4=2 ? Explain.