For which compound inequalities is 6 a solution? Select the statements that are true.(3 points)
Responses
-5 < x < 6
-5 < x < 6
-2 ≤ x ≤ 6
-2 ≤ x ≤ 6
x ≤ 2 or x ≥ 6
x ≤ 2 or x ≥ 6
x < 2 or x > 6
x < 2 or x > 6
x < -5 or x > 0
-5 < x < 6
-2 ≤ x ≤ 6
x ≤ 2 or x ≥ 6
The compound inequalities for which 6 is a solution are:
-2 ≤ x ≤ 6
x ≤ 2 or x ≥ 6
To determine which compound inequalities 6 is a solution for, we need to evaluate each inequality one by one.
1. -5 < x < 6: This inequality states that x is greater than -5 and less than 6. Since 6 is less than 6, it is not a solution for this inequality.
2. -2 ≤ x ≤ 6: This inequality states that x is greater than or equal to -2 and less than or equal to 6. Since 6 is equal to 6, it is a solution for this inequality.
3. x ≤ 2 or x ≥ 6: This inequality represents a range where x is less than or equal to 2, or greater than or equal to 6. Since 6 is greater than or equal to 6, it is a solution for this inequality.
4. x < 2 or x > 6: This inequality represents a range where x is less than 2, or greater than 6. Since 6 is not less than 2 or greater than 6, it is not a solution for this inequality.
5. x < -5 or x > 0: This inequality represents a range where x is less than -5, or greater than 0. Since 6 is neither less than -5 nor greater than 0, it is not a solution for this inequality.
From the given options, the true statements are:
-2 ≤ x ≤ 6
x ≤ 2 or x ≥ 6