Solve for h: 2h/3 – 3/2 = -1/2h + 2 h =

To solve the equation ( frac{2h}{3} – frac{3}{2} = -frac{1}{2}h + 2 ), follow these steps:

1. Eliminate Fractions: First, find a common denominator for all terms. The common denominator for 3 and 2 is 6. So, multiply the entire equation by 6:

[

6 left(frac{2h}{3}right) – 6left(frac{3}{2}right) = 6left(-frac{1}{2}hright) + 6(2)

]

This simplifies to:

[

4h – 9 = -3h + 12

]

2. Combine Like Terms: Now, add (3h) to both sides:

[

4h + 3h – 9 = 12

]

Which simplifies to:

[

7h – 9 = 12

]

3. Isolate (h): Add 9 to both sides:

[

7h = 21

]

4. Solve for (h): Now, divide by 7:

[

h = 3

]

Thus, the solution is ( h = 3 ).