6. which of the following includes 7 as a solution?\nthere are four correct answers.\n$6x + 10 <…

6. which of the following includes 7 as a solution?\nthere are four correct answers.\n$6x + 10 < 40$\n$\\frac{1}{2}x + 2.5 < 8$\n$2x + 8 = -6$\n$12 - 4x < -16$\n$2x - 9 = 5$\n$5x + 2 = 7$\n$-3x + 10 = -11$\n$4x - 1 \\geq 23$

6. which of the following includes 7 as a solution?\nthere are four correct answers.\n$6x + 10 < 40$\n$\\frac{1}{2}x + 2.5 < 8$\n$2x + 8 = -6$\n$12 - 4x < -16$\n$2x - 9 = 5$\n$5x + 2 = 7$\n$-3x + 10 = -11$\n$4x - 1 \\geq 23$

Answer

Explanation:

Step1: Solve each equation/inequality

  • For (6x + 10\lt40): Subtract (10) from both sides: (6x\lt40 - 10), so (6x\lt30). Divide both sides by (6): (x\lt5). (7) is not less than (5).
  • For (\frac{1}{2}x+2.5\lt8): Subtract (2.5) from both sides: (\frac{1}{2}x\lt8 - 2.5=5.5). Multiply both sides by (2): (x\lt11). (7\lt11).
  • For (2x + 8=-6): Subtract (8) from both sides: (2x=-6 - 8=-14). Divide by (2): (x=-7\neq7).
  • For (12-4x\lt - 16): Subtract (12) from both sides: (-4x\lt-16 - 12=-28). Divide by (-4) (reverse inequality sign): (x\gt7). (7) is not greater than (7).
  • For (2x-9 = 5): Add (9) to both sides: (2x=5 + 9 = 14). Divide by (2): (x = 7).
  • For (5x+2 = 7): Subtract (2) from both sides: (5x=7 - 2 = 5). Divide by (5): (x = 1\neq7).
  • For (-3x+10=-11): Subtract (10) from both sides: (-3x=-11 - 10=-21). Divide by (-3): (x = 7).
  • For (4x-1\geq23): Add (1) to both sides: (4x\geq23 + 1=24). Divide by (4): (x\geq6). (7\geq6).

Answer:

(\frac{1}{2}x + 2.5\lt8), (2x-9 = 5), (-3x + 10=-11), (4x-1\geq23)