Question 10819: Please help me solve this equation:
19 -(2x +3) = 2(x + 3) +x
My attempt:
19 - (2x + 3) = 2(x + 3) +x
19 - 2x + 3 = 2x + 3 +x
19 - 2x + 3 = 3x + 3
19 - 2x + 3 - 3x = + 3
19 +3 -3 = +3 -3
19 = x
Found 2 solutions by longjonsilver, WannabeCAgirl83:
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! Sorry, but your attempt is riddled with wrong algebra.
First thing is to understand what the question actually says, because from your working, you do not understand. I think you wildly do stuff and hope for the best.
19 - (2x +3) = 2(x + 3) +x is a shortened version (yes, a lazy version even) for
19 -1*(2x +3) = 2*(x + 3) + 1*x
Mathematicians tend not to write a "1" or a "*" when we do not need too. But you have to remember they are there.
Secondly, you have to know what to do when you have brackets... the second bracker for example says "we have (x+3) and we multiply these terms by 2. So we will get a "2x" and a "6" when we expand the bracket.
Similarly, with the first bracket, we have the (2x+3) and we have to multiply both terms by the -1... giving us -2x and -3. ALWAYS BE CAREFUL with brackets and negatives outside!
So, we get:
19 - (2x +3) = 2(x + 3) + x
19 - 2x - 3 = 2x + 6 + x
Now collect like terms together:
19 - 2x - 3 = 2x + 6 + x
16 - 2x = 3x + 6
Now move terms so that all variables (here, the x-terms) are on one side and the numbers are on the other side:
16 - 2x = 3x + 6 --> Add 2x to both sides.
16 = 5x + 6
or, 5x + 6 = 16
--> now we subtract 6 from both sides to give
5x = 10
--> now, we have 5x, like 5 apples. So, if 5 apples cost 10pence, one apple must cost 2p, yes? How did I do that? I divided both sides by 5.
Why did i divide both sides by 5? because i had 5*x and i want to know 1*x. So i have to mess with the 5 without messing the x, so 5/5 is 1. And the one rule of algebra that i have used abouve too, is that "whatever you do to one side, you HAVE to do to the other side", so we have 10 and must divide that by 5 too.
so, 5x = 10
then x = 10/5
--> x= 2
jon.
Answer by WannabeCAgirl83(35)  (Show Source):
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