To simplify a mathematical expression or equation, we have to perform the operations in the right order, following the order of operations or BIDMAS/BODMAS (Brackets, Indices/Orders, Division/Multiplication, Addition/Subtraction).
Step 1: Distribute the numbers outside the brackets (for each of the three subtraction terms separately).
For the first term, distribute the 2 to each term within the brackets:
2*(4) - 2*q = 8 - 2q
For the second term, distribute the -(-2) to each term within the brackets
(-(-2))*(q) + (-(-2))*(5) = 2q + 10
And for the third term, the negative sign is distributed:
-(3q - 4) = -3q + 4
Step 2: Combine like terms.
The equation now becomes:
8 - 2q + 2q + 10 - 3q + 4
The -2q and 2q terms cancel out:
8 + 10 + 4 - 3q
Step 3: Simplify further by adding the constants and bringing the numeric term on the left:
22 - 3q
Therefore, the simplified equation is 22 - 3q = 0, or, moving the -3q to the right side of the equation to keep q positive:
3q = 22