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
-5 < x < 6
-2 ≤ x ≤ 6
x ≤ 2 or x ≥ 6
To determine which compound inequalities have 6 as a solution, we need to plug in 6 for the variable x and see if the statement is true.
1. -5 < x < 6: Plug in 6 for x:
-5 < 6 < 6
This statement is false since 6 is not less than 6. Therefore, 6 is not a solution to this compound inequality.
2. -2 ≤ x ≤ 6: Plug in 6 for x:
-2 ≤ 6 ≤ 6
This statement is true since 6 is both greater than or equal to -2 and less than or equal to 6. Therefore, 6 is a solution to this compound inequality.
3. x ≤ 2 or x ≥ 6: Plug in 6 for x:
6 ≤ 2 or 6 ≥ 6
This statement is false since neither 6 is less than or equal to 2 nor 6 is greater than or equal to 6. Therefore, 6 is not a solution to this compound inequality.
In summary, the compound inequality -2 ≤ x ≤ 6 has 6 as a solution.
The compound inequalities for which 6 is a solution are:
-2 ≤ x ≤ 6
x ≤ 2 or x ≥ 6