Solve for q.
3 – q = 3/4 + 3/2 q
q = =
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To solve for ( q ) in the equation ( 3 – q = frac{3}{4} + frac{3}{2} q ), let’s follow these steps:
1. First, rearrange the equation to isolate ( q ). Start by getting all the terms with ( q ) on one side:
[
3 – frac{3}{4} = q + frac{3}{2}q
]
2. Calculate ( 3 – frac{3}{4} ):
Convert 3 to have a denominator of 4:
[
3 = frac{12}{4}
]
Thus,
[
frac{12}{4} – frac{3}{4} = frac{9}{4}
]
3. Now, combine the ( q ) terms on the right:
[
q + frac{3}{2}q = frac{2}{2}q + frac{3}{2}q = frac{5}{2}q
]
4. Now, we have the equation:
[
frac{9}{4} = frac{5}{2}q
]
5. To solve for ( q ), multiply both sides by the reciprocal of ( frac{5}{2} ), which is ( frac{