How do I solve an equation with constants in the denominators?

Question

For example, a few problems I have to solve are:

x/2=3x/4+5

2x-2x/7=x/2+17/2

Please explain also the processes you use to solve the problems, and not necessarily just the answers. I have many more problems like these to solve and the purpose of my asking about these two is to understand how to solve them:) Thank You!!!

Answer 1

x/2=3x/4+5

Find the common denominator. (4)

2x/4= 3x/4 + 20/4

2x=3x+20

-x=20

x= -20

2x- 2x/7= x/2+17/2

Find the common denominator. (14)

28x/14 - 4x/14 = 7x/14 + 119/14

28x-4x=7x+119

17x=119

x = 7

Answer 2

ok, for the 1st problem:

so what you want to do first, is make a common denominator for the two fractions. do this by multiplying the left by 2.

2x/4=3x/4+5.

move the 3x/4 to the left, and subract.

2x/4-3x/4=5

-x/4=5

cross multiply

-x=20

x=-20.

to check if this is right, plug it back into the equation.

it works!

try the 2nd prob, and email me if u cant get the rest!

tUNZ

Answer 3

1. x/2=3x/4 + 5

this equation is like saying 1/2X=3/4x + 5

next, we put all values similar to each other on the same side. subtract 3/4x from both sides of the equation: 1/2x - 3/4x = 5

now give 1/2 the same denominator as 3/4. 1/2 is equal to 2/4:

2/4x - 3/4x = 5

now subtract: -1/4x = 5

next divide both sides of the equation by -1/4 : x = 5/(-1/4) = -20

check the answer: (-20)/2 = 3(-20)/4 + 5  :  -10 = -60/4 + 5  :

-10 = -15 + 5   :  -10 = -10

2. 2x - 2x/7 = x/2 + 17/2 :  

get all the x's on the same side: 2x - 2/7x -1/2x = 17/2

find common denominator: 28/14x - 4/14 - 7/14x = 119/14

subtract:17/14x = 119/14

divide: x = (119/14)/(17/14) = (119/14) * (14/17) = 119/17 = 7

check answer: 2(7) - 2(7)/7 = (7)/2 +17/2 : 14 - 2 = 24/2 : 12 = 12