Answer:
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
