Select the correct answer. Which inequality represents all the solutions of -2(3x + 6) ≥ 4(x + 7)?

A. x ≥ -4
B. x ≤ -4
C. x ≥ 8
D. x ≤ 8

Answer is B: x≤-4

Step-by-step explanation:

-2(3x+6)≥4(x+7)

distribute

-6x-12≥4x+28

add 12 on both sides and subtract 4x on both sides

-10x≥40

divide by -10 on both sides. keep in mind that this flips the inequality sign.

x≤-4

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1