Question

what is the value of ( x ) in the inequality: (-4(6 + 5x) - 7 leq -9(2x + 3)) (\bigcirc) ( x geq -2 ) (\bigcirc) ( x leq -8 ) (\bigcirc) ( x leq -2 ) (\bigcirc) ( x geq 6 )

Explanation:

Step1: Expand both sides

First, expand \(-4(6 + 5x)-7\) and \(-9(2x + 3)\).
For the left - hand side:
Using the distributive property \(a(b + c)=ab+ac\), we have \(-4(6 + 5x)-7=-4\times6-4\times5x - 7=-24-20x - 7=-31 - 20x\)
For the right - hand side:
\(-9(2x + 3)=-9\times2x-9\times3=-18x-27\)
So the inequality becomes \(-31 - 20x\leq-18x-27\)

Step2: Isolate the variable \(x\)

Add \(20x\) to both sides of the inequality:
\(-31-20x + 20x\leq-18x-27 + 20x\)
Simplify to get \(-31\leq2x-27\)
Then add 27 to both sides:
\(-31 + 27\leq2x-27 + 27\)
Simplify: \(-4\leq2x\)

Step3: Solve for \(x\)

Divide both sides of the inequality \(-4\leq2x\) by 2:
\(\frac{-4}{2}\leq\frac{2x}{2}\)
Simplify to get \(-2\leq x\), which is equivalent to \(x\geq - 2\)

Answer:

\(x\geq - 2\) (corresponding to the option \(x\geq - 2\))