Question

1. which numbers in the set {2.1, 9\frac{1}{2}, 8} are solutions of the inequality 6 < k - 2? explain.

Explanation:

Step1: Simplify the inequality

First, solve for $k$ by adding 2 to both sides of the inequality to isolate the variable.
$6 + 2 < k - 2 + 2$
$\implies 8 < k$ or $k > 8$

Step2: Test each set value

Check each number in $\{2.1, 9\frac{1}{2}, 8\}$ against $k > 8$:

• For $2.1$: $2.1 > 8$ is false.
• For $9\frac{1}{2} = 9.5$: $9.5 > 8$ is true.
• For $8$: $8 > 8$ is false (the inequality is strict, so equal values do not count).

Answer:

The only solution from the set is $9\frac{1}{2}$, since it is the only number greater than 8, which is the simplified condition of the inequality $6 < k - 2$.