How to solve 5h-2 (3/2h+4) = 10

h = 9

Step-by-step explanation:

Solve for h:

5 h - 2 ((3 h) / 2 + 4) = 10

Put each term in (3 h) / 2 + 4 over the common denominator 2: (3 h) / 2 + 4 = (3 h) / 2 + 8/2:

5 h - 2 (3 h) / 2 + 8/2 = 10

(3 h) / 2 + 8/2 = (3 h + 8) / 2:

5 h - 2 (3 h + 8) / 2 = 10

(-2) / 2 = (2 (-1)) / 2 = - 1:

5 h + - 1 (3 h + 8) = 10

- (3 h + 8) = - 3 h - 8:

5 h + - 3 h - 8 = 10

Grouping like terms, 5 h - 3 h - 8 = (5 h - 3 h) - 8:

(5 h - 3 h) - 8 = 10

5 h - 3 h = 2 h:

2 h - 8 = 10

Add 8 to both sides:

2 h + (8 - 8) = 8 + 10

8 - 8 = 0:

2 h = 10 + 8

10 + 8 = 18:

2 h = 18

Divide both sides of 2 h = 18 by 2:

(2 h) / 2 = 18/2

2/2 = 1:

h = 18/2

The gcd of 18 and 2 is 2, so 18/2 = (2*9) / (2*1) = 2/2*9 = 9:

Answer: h = 9