what value of x is in the solution set of the inequality -2(3x + 2) > -8x + 6? -6 -5 5 6

Explanation:

Step1: Expand the left - hand side

$$-2(3x + 2)=-6x-4$$ The inequality becomes $-6x - 4>-8x + 6$.

Step2: Add (8x) to both sides

$$-6x+8x-4>-8x + 8x+6$$ $$2x-4>6$$

Step3: Add (4) to both sides

$$2x-4 + 4>6+4$$ $$2x>10$$

Step4: Divide both sides by (2)

$$\frac{2x}{2}>\frac{10}{2}$$ $$x > 5$$

Answer:

C. (5) (Note: The options are likely mis - labeled. Since (x>5), if we assume the options are for checking which value satisfies the original inequality when substituted. Let's check each option:

• For (x=-6): (-2(3\times(-6)+2)=-2(-18 + 2)=-2\times(-16)=32), (-8\times(-6)+6=48 + 6=54), (32<54)
• For (x=-5): (-2(3\times(-5)+2)=-2(-15 + 2)=-2\times(-13)=26), (-8\times(-5)+6=40+6 = 46), (26<46)
• For (x = 5): (-2(3\times5+2)=-2(15 + 2)=-34), (-8\times5+6=-40 + 6=-34), (-34=-34) (not (>))
• For (x = 6): (-2(3\times6+2)=-2(18+2)=-40), (-8\times6+6=-48 + 6=-42), (-40>-42))

So the value that satisfies the inequality (if we consider the correct inequality solution (x>5) and check the options by substitution) is (x = 6))