Simplify 6(3q−4)+18−12q−7(4q+5)

Question

6
(
3
𝑞
−
4
)
+
18
−
12
𝑞
−
7
(
4
𝑞
+
5
)
.(1 point)
$$

Answer 1

To simplify the expression \( 6(3q−4) + 18−12q−7(4q+5) \), we start by distributing the terms:

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

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

Now substitute these back into the original expression: \[ 18q - 24 + 18 - 12q - 28q - 35 \]

Next, combine like terms for \(q\) and constant terms:

1. Combine the \(q\) terms: \[ 18q - 12q - 28q = (18 - 12 - 28)q = -22q \]

2. Combine the constant terms: \[ -24 + 18 - 35 = -24 + 18 = -6 \] \[ -6 - 35 = -41 \]

Putting it all together gives: \[ -22q - 41 \]

Thus, the simplified expression is: \[ \boxed{-22q - 41} \]

Answer 2

Simplify 6(3q−4)+18−12q−7(4q+5)

Answer 3

Let's simplify the expression \( 6(3q−4) + 18−12q−7(4q+5) \) step by step.

1. Distributing the terms:

   • For \(6(3q - 4)\): \[ 6 \cdot 3q - 6 \cdot 4 = 18q - 24 \]

   • For \(-7(4q + 5)\): \[ -7 \cdot 4q - 7 \cdot 5 = -28q - 35 \]

2. Substituting back into the expression: \[ 18q - 24 + 18 - 12q - 28q - 35 \]

3. Combining like terms:

   • For the \(q\) terms: \[ 18q - 12q - 28q = (18 - 12 - 28)q = -22q \]

   • For the constant terms: \[ -24 + 18 - 35 = -24 + 18 = -6 \] \[ -6 - 35 = -41 \]

4. Putting it all together: \[ -22q - 41 \]

Therefore, the simplified expression is: \[ \boxed{-22q - 41} \]