here is an inequality: $\\frac{7x + 6}{2} \\leq 3x + 2$\nselect all of the values that are a solution to the…

here is an inequality: $\\frac{7x + 6}{2} \\leq 3x + 2$\nselect all of the values that are a solution to the inequality.\n$\\square x = -3$\n$\\square x = -2$\n$\\square x = -1$\n$\\square x = 0$\n$\\square x = 1$\n$\\square x = 2$\n$\\square x = 3$

here is an inequality: $\\frac{7x + 6}{2} \\leq 3x + 2$\nselect all of the values that are a solution to the inequality.\n$\\square x = -3$\n$\\square x = -2$\n$\\square x = -1$\n$\\square x = 0$\n$\\square x = 1$\n$\\square x = 2$\n$\\square x = 3$

Answer

Explanation:

Step1: Solve the inequality

Multiply both sides by (2) to get (7x + 6\leqslant6x + 4). Subtract (6x) from both sides: (7x-6x+6\leqslant6x - 6x+4), which simplifies to (x+6\leqslant4). Subtract (6) from both sides: (x+6 - 6\leqslant4 - 6), so (x\leqslant-2).

Step2: Check each value

  • For (x=-3): (-3\leqslant-2) (True).
  • For (x = - 2): (-2\leqslant-2) (True).
  • For (x=-1): (-1>-2) (False).
  • For (x = 0): (0>-2) (False).
  • For (x = 1): (1>-2) (False).
  • For (x = 2): (2>-2) (False).
  • For (x = 3): (3>-2) (False).

Answer:

(x=-3), (x = - 2)