Question 765519: Tom was asked to find the solution set for the inequality
6(x+4)-6(x+2)=6(3x+1)-12.
The steps for his solution are shown.
I. x+4-x-2=3x+1-2
II. 2=3x-1
III. 3x= -1-2
IV. x=-1
When he examines his solution, Tom found that his first error was in step
a.I b. II c.III d. IV
I thought that the error was in step I, but the error was actually in step III. I tried to figure out why the error was in step III. I thought the error was in step I because you have to expand but Tom did not expland apparently he divided,, Why did he divide? I thought you have to expand meaning multiply to get x but it self but instead they did not multiply they divided......... My question here is that I want to know why is the error found in III.
Can you please explain and provide a detailed explanation PLZ and thank you.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! In step III it should be -3x = -1-2 or -3x = -3 because you are subtracting 3x from both sides to get it isolated. So that explains why step III is wrong.
There is no error in step 1 because he divided everything (outside the parenthesis) by 6 and distributed the negative through. That's a valid step as long as it is applied to both sides. You could distribute if you want, but he took a different path.
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