Which inequality has solutions that include 12, 13, and 14?(1 point)

Question

Responses

2x≥11+13
2 x greater-than-or-equal-to 11 plus 13

2x<13+15
2 x less than 13 plus 15

2x≥34−6
2 x greater-than-or-equal-to 34 minus 6

2x≤12

Answer 1

To determine which inequality includes the solutions 12, 13, and 14, we can evaluate each option given:

1. \(2x \geq 11 + 13\)

   • Simplifying this gives \(2x \geq 24\).
   • Dividing by 2 gives \(x \geq 12\).
   • This includes 12, 13, and 14.

2. \(2x < 13 + 15\)

   • Simplifying gives \(2x < 28\).
   • Dividing by 2 gives \(x < 14\).
   • This does not include 14.

3. \(2x \geq 34 - 6\)

   • Simplifying gives \(2x \geq 28\).
   • Dividing by 2 gives \(x \geq 14\).
   • This does not include 12 or 13.

4. \(2x \leq 12\)

   • Dividing by 2 gives \(x \leq 6\).
   • This does not include 12, 13, or 14.

Thus, the only inequality that includes 12, 13, and 14 is:

\(2x \geq 11 + 13\) (which simplifies to \(x \geq 12\)).