How to solve linear equations with fractions?

Question

Hey, can anybody show me how to solve these linear equation fractions step by step?

3x+1=1/2

1/4x-5/2=-2

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

Thanks, I just don't understand how to do it.

Answer 1

3x + 1 = 1/2
multiple everything by 2
6x + 2 = 1
6x = -1
x = -1/6

1/4x = x/4
x/4 + 5/2 = -2 multiply everything by 4
x + 20/2 = -8
x + 10 = -8
x = -18

x-5 = 3/2x + 5/2 multiply everything by 2x
2x(x - 5) = 3 + 10x/2
2x^2 - 10X = 3 + 5x
2x^2 - 15x -3 = 0

Answer 2

first get rid of the fractions and then solve
1.3x+1=1/2
multiply both sides by 2
2(3x+1)=2*1/2
6x+2=1
6x=1
x=1/6

2.1/4x-5/2=-2
here the LCD of 4 and 2 is 4,,so multiply
both sides by4
4(1/4)x-4(5/2)=4(-2)
x-10=-8
x=-8+10=2

3.x-5=3/2x+5/2
multiply both sides by 2
2(x-5)=2(-3/2)x+2(5/2)
2x-10=-3x+5
2x+3x=5+10
5x=15
x=3

Answer 3

here u go

1) 3x+1=1/2
3x=1/2-1
3x=-1/2
x=-1/6

2)1/4x-5/2=-2
1/4x=-2+5/2
1/4x=1/2
x=2

3)x-5=-3/2x+5/2
x-5+3/2x=5/2
(2x+3x)/2=5/2+5
5x/2=15/2
5x=15
x=3

Answer 4

3x+1=1/2
3x=1/2-1
3x=-1/2
x=-1/6

1/4x-5/2=-2
1/4x=-2+5/2
1/4x=1/2 (x4 to both sides)
x=2

x-5=-3/2x+5/2
x+3/2x=5/2+5
5/2x=15/2
x=3