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Question 504571: please help can not understand if I am doing this right. Thank you so much
Sovlve the equation:
4 - 8x = 8
x +1 = x +1
Here's what I did
4(x + 2)= 8
(x +1)(x -1) = x + 1
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you have 4 - 8x = 8
subtract 4 from both sides of that equation to get:
-8x = 8 - 4 which becomes:
-8x = 4
multiply both sides of the equation by -2 to get:
8x = -4
divide both sides of the equation by 8 to get:
x = -4/8
this reduces to:
x = -1/2
substitute for x in the original equation of:
4 - 8x = 8 to get:
4 - 8(-1/2) = 8 which becomes:
4 - (-8/2) = 8 which becomes:
4 + 8/2 = 8 which becomes:
4 + 4 = 8 which is true, so the value of x = -1/2 is good.
your second equation is:
x+1 = x+1
subtract x from both sides of the equation to get:
x - x + 1 = 1
subtract 1 from both sides of the equation to get:
x - x = 1 - 1
combine like terms to get:
0 = 0
the variable x dropped out of the equation and the equation is still true so the original equation is an identity and any value of x will satisfy it.
when you're solving equations, whatever you do to the left side of the equation has to be done to the right side of the equation as well.
the purpose is to isolate the unknown variable to one side of the equation with all the rest on the other side of the equation.
you were able to do that with the first problem.
you tried to do that with the second problem but the variable disappeared.
that's ok.
if the variable disappears and the equation is true (3 = 3, 0 = 0, etc), then any value of x will solve the equation.
if the variable disappears and the equation is false (3 = 2, 0 = 15), etc), then no value of x will solve the equation.
an example of an invalid equation would be:
x+1 x+5
subtract x from both sides of this equation to get:
1 = 5
this is clearly not true, so the equation is invalid and no value of x will satisfy it.
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