Question

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 1

A. x > -4

Step-by-step explanation:

-2(3x+6) < 4(x + 7)

-6x - 12 < 4x + 28 [expand brackets]

-10x < 40 [Combine like terms

x > -4 [Divide both sides by -10. The inequality is reversed when dividing by a negative number.]

Answer 2

The inequality representing the solutions of the given expression is x > -4.

Step-by-step explanation:

To solve the inequality -2(3x+6) < 4(x + 7), we need to distribute the coefficients and simplify. This gives us -6x - 12 < 4x + 28. Next, we can combine like terms by adding 6x to both sides of the inequality. This gives us -12 < 10x + 28. Then, we can subtract 28 from both sides of the inequality. This gives us -40 < 10x. Finally, we can divide both sides of the inequality by 10 to get the value of x. This gives us -4 < x. Therefore, the inequality representing all the solutions is x > -4, which corresponds to option A.