Simplify 6(3q−4)+18−12q−7(4q+5)

1 answer

To simplify the expression \( 6(3q - 4) + 18 - 12q - 7(4q + 5) \), we will follow the order of operations by distributing the coefficients and combining like terms.

  1. Distribute \( 6 \) into \( (3q - 4) \): \[ 6 \cdot 3q - 6 \cdot 4 = 18q - 24 \]

  2. Distribute \( -7 \) into \( (4q + 5) \): \[ -7 \cdot 4q - 7 \cdot 5 = -28q - 35 \]

  3. Substitute these back into the expression: \[ 18q - 24 + 18 - 12q - 28q - 35 \]

  4. Combine like terms. First, combine the \( q \) terms: \[ 18q - 12q - 28q = (18 - 12 - 28)q = -22q \]

  5. Next, combine the constant terms: \[ -24 + 18 - 35 = -6 - 35 = -41 \]

  6. Putting it all together, the simplified expression is: \[ -22q - 41 \]

Thus, the final answer is: \[ \boxed{-22q - 41} \]