Question

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

Answer 1

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