please help trying to help daughter?

Question

been out of school for 21 years trying to learn how to solve equations with fractions example 2/x+5/2=4-2/3x

Answer 1

A good first step for dealing with fractions is to find a common denominator. Typically you can multiply through by it and get rid of the fractions. In this case the denominators are x, 2, and 3x, so if we multiply through by 6x, we get rid of the fractions and get:

12 + 15x = 24x - 4

I am guessing you can probably take it from here, but just as a check, collecting terms you get: 16 = 9x, and then x = 16/9. Then if you like you can plug that into the original equation to check your work.

Hope that helps!

Answer 2

are you solving for x?
and is the last term (2/3)x or (2/(3x))? this can change the answer.

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

First, combine like terms:
2/x + 2/3x = 4 - (5/2)

Use least common denominator to make them combinable:
(2/x)(3/3) + 2/3x = 1.5

6/3x + 2/3x = 1.5

(6+2)/3x = 1.5

8/3x = 3/2

Cross multiply to find x:
8*2 = 3*3x

16 = 9x

16/9 = x

Answer 3

ok. find the least common denominator:

the current denominators are:

x; 2; 1; 3x

the LCD is 6x.

Multiply each term by that:

6x (2/x) + 6x(5/2)=6x(4) - 6x (2/3x)

12 + 15x = 24x - 4

Now add 4 to both sides and subtract 15x from both sides

16 = 9x

x = 9/16

Answer 4

the slowest method i find the easiest, that is to multiply the entire thing by one denominator at a time

2/x +5/2=4+(2/3)x miltiply by x
2+(5x)/2=4x+(2/3)x^2 multiply by 2
4+5x=8x+(4/3)x^2 multiply by 3
12+15x=24x+4x^2 take everything to one side
4x^2+9x-12=0

Answer 5

multiply both sides by x to get
2+5x/2=4x-2/3
Now bring x to one side and the constants to the other side
2+2/3=4x-5x/2
To make it easier, I'll deal with improper fractions
8/3=3x/2
x=8/3*2/3=16/9
check
2+80/18?=?64/9-2/3
36/18+80/18=116/18=58/9
64/9-6/9=58/9
It works!