which of the x values are solutions to the inequality 4(2 - x) > -2x - 3(4x + 1)? check all that apply.\n□ x…

which of the x values are solutions to the inequality 4(2 - x) > -2x - 3(4x + 1)? check all that apply.\n□ x = -1.1\n□ x = -2.2\n□ x = 0\n□ x = -10\n□ x = 10

which of the x values are solutions to the inequality 4(2 - x) > -2x - 3(4x + 1)? check all that apply.\n□ x = -1.1\n□ x = -2.2\n□ x = 0\n□ x = -10\n□ x = 10

Answer

Answer:

  • A. $x = - 1.1$
  • C. $x = 0$
  • E. $x = 10$

Explanation:

Step1: Expand both sides

Expand $4(2 - x)$ to get $8-4x$, and expand $-2x - 3(4x + 1)$ to $-2x-12x - 3=-14x - 3$. So the inequality becomes $8-4x>-14x - 3$.

Step2: Move x - terms to one side

Add $14x$ to both sides: $8-4x + 14x>-14x - 3+14x$, which simplifies to $8 + 10x>-3$.

Step3: Move constant to the other side

Subtract 8 from both sides: $8 + 10x-8>-3 - 8$, resulting in $10x>-11$.

Step4: Solve for x

Divide both sides by 10: $x>-\frac{11}{10}=-1.1$.

  • For $x=-1.1$, $-1.1\not> - 1.1$, so it's not a solution.
  • For $x=-2.2$, $-2.2\not> - 1.1$, so it's not a solution.
  • For $x = 0$, $0>-1.1$, so it's a solution.
  • For $x=-10$, $-10\not> - 1.1$, so it's not a solution.
  • For $x = 10$, $10>-1.1$, so it's a solution.