Solve for q. 3/2 – 5/4q + 2/3q – 5/6 = -q q =

To solve the equation ( frac{3}{2} – frac{5}{4}q + frac{2}{3}q – frac{5}{6} = -q ), let’s follow these steps:

1. Combine like terms: Start by moving all ( q ) terms to one side and constant terms to the other.

The equation can be rearranged as:

[

-frac{5}{4}q + frac{2}{3}q + q = frac{3}{2} – frac{5}{6}

]

2. Convert constants: Find a common denominator for the numbers on the right side. The common denominator for ( 2 ) and ( 6 ) is ( 6 ):

[

frac{3}{2} = frac{9}{6}

]

Now, replace it in the equation:

[

-frac{5}{4}q + frac{2}{3}q + q = frac{9}{6} – frac{5}{6}

]

Simplifying the right side gives:

[

frac{9 – 5}{6} = frac{4}{6} = frac{2}{3}

]

3. Combine ( q ) terms: Convert all coefficients of ( q