8
algebra

Which value is in the solution set of 2x372x - 3 \geq 7?

A

x=4x = 4

B

x=5x = 5

C

x=3x = 3

D

x=2x = 2

Correct Answer: B

Choice B is the correct answer. First solve the inequality to find the solution set.

  1. Add 3: 2x3+37+32x - 3 + 3 \geq 7 + 3, giving 2x102x \geq 10
  2. Divide by 2: x5x \geq 5
  3. Check choices: x=5x = 5 is the minimum value that satisfies x5x \geq 5
  4. Verify: 2(5)3=103=772(5) - 3 = 10 - 3 = 7 \geq 7 ??n ?�� Strategic Tip: The boundary value (here, 5) satisfies \geq but not >> inequalities.

Choice A is incorrect becausex=4x = 4 does not satisfy x5x \geq 5 (4 is less than 5). Choice C is incorrect becausex=3x = 3 is below the solution range. Choice D is incorrect becausex=2x = 2 is well below the minimum value of 5.