Simplify 6(3q−4)+18−12q−7(4q+5) .
To simplify the expression 6(3q - 4) + 18 - 12q - 7(4q + 5), we will follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
First, let's simplify what is inside the first set of parentheses: 3q - 4.
Next, we multiply 6 by the simplified expression inside the parentheses: 6 * (3q - 4) = 18q - 24.
Next, we simplify what is inside the second set of parentheses: 4q + 5.
Next, we multiply 7 by the simplified expression inside the parentheses: 7 * (4q + 5) = 28q + 35.
Now, we substitute the simplified expressions back into the original expression to get: 18q - 24 + 18 - 12q - 28q - 35.
Next, we combine like terms. Combining the q terms, we have: 18q - 12q - 28q = -22q.
Next, combining the integer terms, we have: -24 + 18 - 35 = -41.
Finally, substituting the simplified terms back into the original expression, we have: -22q - 41.