Question

jay thinks that the inequality k< 3 implies the inequality k squared < 9 but val thinks otherwise. Who is right and why

Answer 1

Answer:

  Val is right

Step-by-step explanation:

One of the solutions to k < 3 is k = -4. When you square that, you get ...

  k² = (-4)² = 16

which is not less than 9.

_____

k < 3 and k² < 9 will have the same solution set for |k| < 3, but their solution sets will differ for k ≤ -3.

When performing operations on inequalities, one needs to be aware of the order preserving/changing effects of the operation. Whether squaring a value preserves order or not depends on the relative magnitudes:

• 2 > 1; 2² > 1²
• -1 < 1; (-1)² = 1²
• -2 < 1; (-2)² > 1²
• -2 < -1; (-2)² > (-1)²