Question

1. which set of numbers only contains numbers that make the inequality true?

x + 19 < 28
{10, 11, 12, 13}
{12, 13, 14, 15}
{7, 8, 9, 10}
{3, 4, 5, 6}

Explanation:

Step1: Solve the inequality

To solve \( x + 19 < 28 \), subtract 19 from both sides:
\( x + 19 - 19 < 28 - 19 \)
\( x < 9 \)

Step2: Check each set

• For \(\{10, 11, 12, 13\}\): All numbers \( \geq 10 \), which are \( \geq 9 \). Not valid.
• For \(\{12, 13, 14, 15\}\): All numbers \( \geq 12 \), which are \( \geq 9 \). Not valid.
• For \(\{7, 8, 9, 10\}\): 9 and 10 are \( \geq 9 \). Not valid.
• For \(\{3, 4, 5, 6\}\): All numbers \( < 9 \). Valid.

Answer:

\(\{3, 4, 5, 6\}\) (the last option)