Solve algebraically....?

Question

5 - (2/x-6) = (10-2x) / (x-6)


3/4 = 1- (3x-2) / (x+1)

I asked it a little while ago, but it didn't show up right, so people were getting confused. Sorry. Thanks for all the help. I appreciate it. Even if you don't want to do these exact problems, can you do two, that are similar so I can figure it out myself?

Sam, you just typed the same exact thing I did.. how is that helping me?

Answer 1

for the first 1:
simply multiple both sides by x/6 which would give u:
5x - 30 - 2 = 10 - 2x
5x - 32 = 10 - 2x
7x = 42
x = 6

for the 2nd 1:
multiply both sides by 4
3 = 4 - 4(3x-2)/(x+1)
now multiply both sides by (x+1)
3x + 3 = 4x + 4 - 12x + 8
3x + 3 = -8x + 12
11x = 9
x = 9/11

this answer is 100% correct, btw sam was pretty good but messed up in the last few steps. there is a calculation error in the 2nd last step.

remember to eliminate the fractions in the first step. eliminating fractions makes the job easier. its easy to get rong answers by using fractions and besides, who wants to be messed with fractions?

Answer 2

5 - (2 / x-6) = (10 - 2x) / (x - 6)
Take (x - 6) as common denominator an simplify it.
[5(x - 6) - 2] / (x - 6) = (10 - 2x) / (x - 6)
(5x - 30 - 2) / (x - 6) = (10 - 2x) / (x - 6)
You have (x - 6) as denominator in both sides. They cancel each other.
5x - 32 = 10 - 2x
7x = 22
x = 22/7

3/4 = 1- (3x - 2) / (x + 1)
3/4 = [1(x + 1) - (3x - 2)] / (x + 1)
3/4 = (x + 1 - 3x +2) / (x+1)
3 (x+1) = 4 (3 - 3x)
3x + 3 = 12 - 12x
3x + 12x = 12 - 3
15x = 9
x = 9/15 = 3/5

Answer 3

5 - 2 / (x - 6) = 2(5 - x) / (x - 6)
5 (x - 6) - 2 = 10 - 2x
5x - 30 - 2 = 10 - 2x
7x = 42
x = 6

3(x + 1) = 4(x + 1) - 4 (3x - 2)
3x + 3 = 4x + 4 - 12x + 8
11x = 9
x = 9 / 11

Answer 4

The first eq.
if the equation
5-2/(x-6)=(10-2x)/(x-6 ) {*(x-6)}
5(x-6)-2=10-2x
5x-30-2=10-2x {the var. at one side}
5x+2x=10+30+2
7x=42 {/7}

x= 6

the second eq:
3/4=1-(3x-2)/(x+1)
3/4-1=-(3x-2)/(x+1)
1-3/4=(3x-2)/(x+1)
1/4=(3x-2)/(x+1)

x+1=4(3x-2)
x+1=12x-8
x-12x=-8-1
-11x=-9
x=9/11

Answer 5

5/1-2/ x-6=5(x-6)-2/x-6=3
3/1=10-2x / x-6
10-2x=3x-18
28=5x
x=5.6
----------------------------------------
3/4=1-(3x-2)/x+1
3(x+1) = 4(-3x+2)
3x+3=-12x+8
15x=5
x=3