Solve for q. 3 – q = 3/4 + 3/2 q q =

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{