Question 1016241: Hi I need help with this math question which is Solve for the unknown variable
7x+8-2x= -5x-14+x I have tried this but I am not sure if it is right
7x-2x+8= -5x-14+x
5x-6= -5x+x
5x-4x= 6
x= 6
Found 2 solutions by Theo, macston:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! start with 7x + 8 - 2x = -5x - 14 + x
combine like terms to get 5x + 8 = -4x - 14
add 4x to both sides of the equation and subtract 8 from both sides of the equation to get 5x + 4x = -14 - 8
combine like terms to get 9x = -22
divide both sides of the equation by 9 to get x = -22/9.
if this is correct, you should be able to replace x in your original equation by -22/9 and the equation should be true.
your original equation is 7x + 8 - 2x = -5x - 14 + x
when you replace x with -22/9, this equation becomes -4.2222... = -4.2222...
since the values are the same, the equation is true and your solution is good.
i'm looking at what you did to see where you went wrong.
you did the following:
7x+8-2x= -5x-14+x
this part's ok.
7x-2x+8= -5x-14+x
this part's still ok.
5x-6= -5x+x
you went wrong here.
looks like you subtracted 14 from 8 to get -6.
you should have added 14 to both sides to get 22.
added 14 to both sides to get 8 + 14 = 22
that would have left you with:
5x + 22 = -5x + x
5x - 4x = 6
you perpetuated your mistake.
you should have started with 5x + 22 = -5x + x
when you combine like terms, you should have finished with:
5x + 22 = -4x
you would then have had to add 4x to both sides to get 9x + 22 = 0
you then needed to subtract 22 from both sides to get 9x = -22
you then needed to divide both sides by 9 to get x = -22/9
your problem appears to be in how to move from one side of the equation to the other.
the operation you have to perform is the opposite to the sign that you have.
5x = -4x
to mode 4x from the right side of the equation to the left side of the equation,k you have to add 4x to both sides of the equation.
you will get 5x + 4x = -4x + 4x
the -4x and the + 4x on the right cancel out and you are left with 5x + 4x = 0
you add 5x and 4x together and you get 9x = 0.
same way with 8 = -14
you have to add 14 to both sides of the equation (opposite sign to what needs to be moved).
you would get 8 + 14 = -14 + 14
the -14 + 14 on the right cancel out and you are left with 8 + 14 = 0 which becomes 22 = 0.
it appears to me that's where you went wrong.
here's a reference that might help:
http://www.regentsprep.org/regents/math/algebra/ae2/lsolveq.htm
you do what is called opposite operations.
if a*b = 5 and you want to move a to the right, you divide both sides of the equation by a.
if b/a = 5 and you want to move a to the right, you multiply both sides of the equation by a.
if b + a = 5 and you want to move a to the right, you subtract a from both sides of the equation.
if b - a = 5, and you want move a to the right, you add a to both sides of the equation.
if you've got a^2 = 25 and you want to solve for a, you take the square root of both sides of the eqution to get a = plus or minus square root 9f 25.
Answer by macston(5194)  (Show Source):
You can put this solution on YOUR website! .
7x+8-2x= -5x-14+x
7x-2x+8= -5x-14+x . Problem: ADD 14 to each side.
5x-6= -5x+x . Problem: ADD (4x+22) to each side
5x-4x= 6
x= 6
To check, plug 6 into original equation.(It doesn't work)
.
Correct:
7x+8-2x=-5x-14+x . Combine like terms.
5x+8=-4x-14 . Add 4x to each side.
9x+8=-14 . Subtract 8 from each side.
9x=-22 . Divide each side by 9.
x=(-22/9)
.
CHECK:
.
7x+8-2x=-5x-14+x
7(-22/9)+(72/9)-2(-22/9)=-5(-22/9)-(126/9)+(-22/9)
(-154+72+44)/9=(110-126-22)/9
-38=-38
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