Question

$\frac{5}{2} \times \frac{-5 - 2x - 3 - 4}{6} \times (-x - 2)$

Explanation:

Step1: Rewrite the given expression

The expression is $\frac{5x - (2x - 5 - 2 - 3 - x)}{2} \times 6 \times (-x - 2)$
First simplify the numerator inside the fraction:
Combine like terms in $5x - (2x - 5 - 2 - 3 - x)$:
First simplify the parentheses: $2x - x -5-2-3 = x -10$
So the numerator becomes $5x - (x - 10) = 5x -x +10 = 4x +10$

Step2: Simplify the fraction

$\frac{4x +10}{2} = 2x +5$

Step3: Multiply with remaining terms

Now multiply by $6 \times (-x -2)$:
First multiply $(2x +5) \times 6 = 12x +30$
Then multiply by $(-x -2)$:
$(12x +30)(-x -2) = 12x(-x) +12x(-2) +30(-x) +30(-2)$
$= -12x^2 -24x -30x -60$

Step4: Combine like terms

$-12x^2 + (-24x -30x) -60 = -12x^2 -54x -60$

Answer:

$-12x^2 -54x -60$