For which compound inequalities is 6 a solution? Select the statements that are true.(3 points) Responses
-5 < x < 6
-2 ≤ x ≤ 6
x ≤ 2 or x ≥ 6
x < 2 or x > 6
x < -5 or x > 0
The true statements are:
-5 < x < 6
-2 ≤ x ≤ 6
x < -5 or x > 0
To determine which compound inequalities have 6 as a solution, we need to check if the value of 6 satisfies the inequality.
-5 < x < 6: In this inequality, 6 is not included, so it is not a solution.
-2 ≤ x ≤ 6: In this inequality, 6 is included, so it is a solution.
x ≤ 2 or x ≥ 6: In this inequality, 6 is not included in either option, so it is not a solution.
x < 2 or x > 6: In this inequality, 6 is not included in either option, so it is not a solution.
x < -5 or x > 0: In this inequality, 6 is not mentioned, so it is not a solution.
Based on these evaluations, the true statements are:
-2 ≤ x ≤ 6
To determine which compound inequalities have 6 as a solution, we can substitute 6 into each inequality and see if the statement is true.
1. -5 < x < 6:
Substituting 6, we get: -5 < 6 < 6, which is false.
Therefore, -5 < x < 6 is not true.
2. -2 ≤ x ≤ 6:
Substituting 6, we get: -2 ≤ 6 ≤ 6, which is true.
Therefore, -2 ≤ x ≤ 6 is true.
3. x ≤ 2 or x ≥ 6:
Substituting 6, we get: 6 ≤ 2 or 6 ≥ 6, which is false.
Therefore, x ≤ 2 or x ≥ 6 is not true.
4. x < 2 or x > 6:
Substituting 6, we get: 6 < 2 or 6 > 6, which is false.
Therefore, x < 2 or x > 6 is not true.
5. x < -5 or x > 0:
Substituting 6, we get: 6 < -5 or 6 > 0, which is false.
Therefore, x < -5 or x > 0 is not true.
Based on our analysis, the compound inequality -2 ≤ x ≤ 6 is the only statement that is true and has 6 as a solution.