Solve for h.
2h/3 – 3/2 = -1/2h + 2
h =
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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 ).