solve for x:  5x/x-2 -7=10/x-2

Expert Answers
caledon eNotes educator| Certified Educator

(5x/x-2) - 7 = (10/x-2)

Add 7 to both sides

(5x/x-2) = (10/x-2) + 7

Multiply both sides by (x-2)

5x = 10 + 7x - 14

Simplify

5x = 7x - 4

X = 2

However this doesn't satisfy the original equation; we end up dividing by 0. This is easier to see in a graph;

Both equations have an asymptote at x=2.

Thus, the solution to this problem is not a specific value of x, because all X values are permitted except the value 2. Thus we would say that the domain is x `!=` 2, or that a vertical asymptote is located at x=2

tonys538 | Student

Solving 5x/x-2 -7=10/x-2, the equation is either:

`(5x)/(x-2) -7=10/(x-2)` or `(5x)/(x-2 -7)=10/(x-2)`

`(5x)/(x-2) -7=10/(x-2)`

=> `(5x)/(x-2) - 10/(x - 2) = 7`

=> `(5x - 10)/(x - 2) = 7`

=> `(5*(x - 2))/(x - 2) = 7`

=> 5 = 7

But this is not true.

So the equation `(5x)/(x-2) -7=10/(x-2)` has no solution

`(5x)/(x-2 -7)=10/(x-2)`

=> `(5x)*(x - 2) = 10*(x-2 -7)`

=> `5x^2 - 10x = 10x - 90`

=> `5x^2 - 20x + 90 = 0`

=> `x^2 - 4x + 18 = 0`

=> `x = 2+- sqrt 14*i`

sid-sarfraz | Student

5x/x-2 -7=10/x-2

SOLUTION:-

(5x/x-2) -7 = 10/x-2

Transfer -7 to RHS;

5x/x-2 = (10/x-2) +7

Equal denominator of RHS;

5x/x-2 = {10 + 7(x-2)}/x-2

5x/x-2 = 10+7x -14/x-2

Cancel x-2 from both sides;

5x = 10 + 7x - 14

5x = -4 + 7x

Bring -4 on LHS and 5x on RHS;

4 = 7x - 5x

4 = 2x

x = 4/2

x = 2

Hence Solved!

malkaam | Student

solve for x:  5x/x-2 -7=10/x-2

To solve this the variable x needs to be isolated, therefore,
 
5x/x-2 - 7 = 10/x-2
(5x/x-2 - 7) * x-2 = 10/x-2 * x-2      multiply both sides by x-2
5x - 7x + 14 = 10
-2x + 14 = 10
-2x + 14 - 14 = 10 - 14                     subtract 14 from both sides
-2x = -4 
-2x/-2 = -4/-2                                  Divide both sides by -2
x = 2 Answer.
 
 
 
 
 
 
 
udonbutterfly | Student

5x/x-2 -7=10/x-2

Okay so our goal here is find the LCD of the entire equation. The LCD is x-2 which is going to be multiplied on both sides of the equation.

x-2(5x/x-2 -7) = (10/x-2) x-2

so you distribute and you will get

5x(x-2)/x-2 -7(x-2) = 10(x-2)/x-2 Now the denominators on both side cancel each other out and you will have

5x -7(x-2) = 10 Now distribute the seven amongst the x-2.

5x -7x +14 =10 Add like terms!

-2x + 14 = 10 Now subtract 14 to the right side of the equation

-2x = -4 Now divide -2 on both sides of the equation

x= 2 (remember two negatives being divided or multiplied makes a positive)

jess1999 | Student

To solve for x in the equation 5x/x-2 -7=10/x-2

[5x/x-2] - 7 = 10/x-2

Since 7 isn't useful on the left side you can add it to both side

5x/x-2 = 10/x-2 + 7 Both of the equation ends with x-2 [the denominator] You would multiply both sides by it.

x-2/1[5x/x-2] = [10/x-2] + 7 x-2/1

5x = 10+ 7x-14 Remeber to do the same for the 7.

        -2x =-4 Now divide both sides by -2 to get x by iteself

x = 2

glendamaem | Student

(5x)/(x-2) -7=10/(x-2) 

(5x)/(x-2) -7 + 7=10/(x-2) + 7

(5x)/(x-2) =10/(x-2) +7

(5x)/(x-2) * (x-2) =10/(x-2) * (x-2) + 7 * (x-2)

5x = 10 + 7x -14

5x - 7x = 10 - 14

-2x = -4

x = 2 

atyourservice | Student

`(5x)/(x-2) -7=10/(x-2) `

multiply both sides by x-2 this will cancel out the x-2 denominators:

`(x-2)((5x)/(x-2)) -7=(x-2)(10/(x-2))`

 the problem will become:

5x - 7x + 14 = 10

move like terms to the same side:

5x - 7x = 10 - 14

-2x = -4

divide by -2:

x = 2

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