Question

prepare
determine the parts of the solution set that make each inequality true.
solution set: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

1. ( x > 6 )
2. ( x + 2 > 6 )
3. ( 2x + 2 > 6 )
4. ( 6 < 2(x + 2) - 4 )

Explanation:

Problem 1: \( x > 6 \)

Step1: Identify numbers >6 in the set

The solution set is \(\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\}\). We need to find elements \( x \) where \( x > 6 \).
Numbers greater than 6 in the set are 7, 8, 9, 10, 11, 12, 13, 14, 15.

Step1: Solve the inequality for x

Subtract 2 from both sides: \( x + 2 - 2 > 6 - 2 \) → \( x > 4 \).

Step2: Find x>4 in the set

From \(\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\}\), numbers greater than 4 are 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.

Step1: Solve the inequality for x

Subtract 2: \( 2x + 2 - 2 > 6 - 2 \) → \( 2x > 4 \). Divide by 2: \( x > 2 \).

Step2: Find x>2 in the set

From the set, numbers greater than 2 are 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.

Answer:

\(\{7, 8, 9, 10, 11, 12, 13, 14, 15\}\)

Problem 2: \( x + 2 > 6 \)