For which compound inequalities is 6 a solution? Select the statements that are true
-5< x <6
x<2 or x>6
x< -5 or x >0
-5 < x < 6
x < 2 or x > 6
To determine which compound inequalities have 6 as a solution, we can substitute 6 for x in each of the inequalities and see if it satisfies the inequality. Let's go through each statement:
-5 < x < 6:
6 is not less than -5, so this inequality is false.
x < 2 or x > 6:
Substituting x = 6, we get 6 < 2 or 6 > 6. The first part, 6 < 2, is false. However, the second part, 6 > 6, is also false. So this inequality is false as well.
x < -5 or x > 0:
Substituting x = 6, we get 6 < -5 or 6 > 0. Both parts, 6 < -5 and 6 > 0, are false. So this inequality is false.
In conclusion, none of the statements are true. The compound inequalities do not have 6 as a solution.
To determine which compound inequalities have 6 as a solution, you need to substitute 6 into each inequality and check if the statement is true or false.
1. -5 < x < 6:
When we substitute x = 6 into this inequality, it becomes -5 < 6 < 6, which is false because 6 is not less than itself. Therefore, this statement is false.
2. x < 2 or x > 6:
When we substitute x = 6 into this inequality, we get 6 < 2 or 6 > 6. The first statement, 6 < 2, is false, but the second statement, 6 > 6, is also false. Therefore, the entire compound inequality is false.
3. x < -5 or x > 0:
When we substitute x = 6 into this inequality, it becomes 6 < -5 or 6 > 0. Both statements are true because 6 is greater than -5 and greater than 0. Therefore, this compound inequality is true.
Therefore, the statements that are true and have 6 as a solution are: x < -5 or x > 0.