help with these math problems please.?

Question

1/2 - x/5=2


3/4 + x/3=6


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

if possible explain or give details on how to solve for x.

most detailed gets point

Answer 1

In each case, get rid of the denominators by multiplying both sides by the least common denominator.

1. 1/2 - x/5 = 2. least common denominator = 10
10(1/2 - x/5) = 10(2)
10(1/2) - 10(x/5) = 20
5 - 2x = 20, so -2x = 15, and x = -15/2

2. 3/4 + x/3 = 6. Use 12
12(3/4) + 12(x/3) = 12(6)
9 + 4x = 72, so 4x = 63, and x = 63/4

3. 3 - 2x/5 + 3x/4 = 2. Use 20
20(3) - 20(2x/5) + 20(3x/4) = 20(2)
60 - 8x + 15x = 20
7x = -40, so x = -40/7

Answer 2

1/2 -x/5 = 2
multiply by 10 -> 5 - 2x =20
2x = 5 -20 = -15

x = -7.5

3/4 + x/3 = 6
multiply by 12 -> 3*3 + 4x = 6*12
9 + 4x = 72
4x = 63
x= 15.75

3 - 2x/5 + 3x/4 =2
multiply by 20
3*20 -2x*4 + 3x*5 = 2*20
60 - 8x + 15x =40
20 + 7x = 0
7x = -20
x = -20/7

Answer 3

2. 3/4 + x/3 = 6

First: eliminate fractions - multiply the denominators with each term.

(3)(4)(3/4)+(3)(4)(x/3) = (3)(4)(6)

*Cross cancel the same terms; combine the rest.

(3)(3)+(4)(x) = (3)(4)(6)
9 + 4x = 72

Sec: combine "like" terms - subtract 9 from both sides (when you move a term to the opposite side, always use the opposite sign).

9-9+ 4x = 72-9
4x = 63 > divide both sides by 4.
4x/4 = 63/4

*Follow the same method to solve the rest.

Answer 4

1/2-x/5=2
-1/2 -1/2
-x/5=3/2
(-5)*-x/5=3/2*(-5)
x=-(15/2)

3/4+x/3=6
-3/4 -3/4
x/3=21/4
(3)*x/3=(21/4)*3
x=63/4

3-2x/5+3x/4=2
+3 +3
3x/4-2x/5=5
x((3/4)-(2/5))=5
x((15/20)-(8/20))=5
x(7/20)=5
(20/7)*x(7/20)=5*(20/7)
x=100/7

* indicates multiplication