Question

1. which set of numbers only contains solutions to the inequality?

x - 12 ≤ 7
{19,21,23}
{10,20,30}
{4,25,36}
{2,14,19}

Explanation:

Step1: Solve the inequality

To solve \( x - 12 \leq 7 \), add 12 to both sides:
\( x - 12 + 12 \leq 7 + 12 \)
\( x \leq 19 \)

Step2: Check each set

• For \(\{19, 21, 23\}\): \(21 > 19\), \(23 > 19\) → Not all solutions.
• For \(\{10, 20, 30\}\): \(20 > 19\), \(30 > 19\) → Not all solutions.
• For \(\{4, 25, 36\}\): \(25 > 19\), \(36 > 19\) → Not all solutions.
• For \(\{2, 14, 19\}\): \(2 \leq 19\), \(14 \leq 19\), \(19 \leq 19\) → All satisfy \(x \leq 19\).

Answer:

\(\{2, 14, 19\}\) (the last option)