Help with some math problems?

Question

1. x/3 + x/4 = 2

2. 2y/3 - y/5 = 4

3. n + 3/2 5 (5 is next to the fraction) = 15

4. x+1/4 + 2x+5/3 = 1/12

5. c+2/2 - 4 = c - 1/3

Answer 1

1.

x/3 + x/4 = 2   ...factor out an x on the left side

x(1/3 + 1/4) = 2

x(7/12) = 2   ...multiply both sides by 12

7x = 24   ...divide both sides by 7

x = 24/7

2.

2y/3 - y/5 = 4   ...factor out a y on the left sides

y(2/3 - 1/5) = 4

y(7/15) = 4   ...multiply both sides by 15

7y = 60   ...divide both sides by 7

y = 60/7

3. By 5 is next to the fraction do you mean 5 + 3/2 as in 5 and three halves?

n + 3/2 5 (5 is next to the fraction) = 15

n + 5 + 3/2 = 15   ...subtract 5 from both sides

n + 3/2 = 10   ...subtract 3/2 from both sides

n = 20/2 - 3/2

n = 17/2

4.  I'm guessing what you wanted in the denominator of these fractions.

(x + 1)/4 + (2x + 5)/3 = 1/12  

x/4 + 1/4 + 2x/3 + 5/3 = 1/12   ...subtract 1/4 from both sides

x/4 + 2x/3 + 5/3 = -1/6   ...subtract 5/3 from both sides

x/4 + 2x/3 = -11/6   ...factor out an x on the left side

x(1/4 + 2/3) = -11/6

x(11/12) = -11/6   ...multiply both sides by 12

11x = -22   ...divide both sides by 11

x = -2

5.  I assume you wanted to add parentheses to have c + 2 be the numerator of the fraction.  I have added them below.

(c + 2)/2 - 4 = (c - 1)/3

c/2 + 2/2 - 4 = c/3 - 1/3

c/2 + 1 - 4 = c/3 - 1/3

c/2 - 3 = c/3 - 1/3   ...add 3 to both sides

c/2 = c/3 - 1/3 + 3   ...subtract c/3 from both sides

c/2 - c/3 = 8/3   ...factor out a c on the left side

c(1/2 - 1/3) = 8/3

c(1/6) = 8/3   ...multiply both sides by 6

c = 16

Hope this helps you!