The three-part inequality a < x ¡Ü b means "a is less than x and x is less than or equal to b". Which of these inequalities is not satisfied by any real number x?
(a) -5 < x ¡Ü -11
(b) -8 < x ¡Ü -7
(c) 0 < x ¡Ü 4
(d) -2 < x ¡Ü 6
How can x be greater than -5 and less than or equal to -11? Think about it.
I thought the answer was A as well. X can not be greater than 5 and less than or = to - 11 so A is the answer?
To determine which inequality is not satisfied by any real number x, we can examine each option and check for any inconsistencies.
(a) -5 < x ≤ -11
In this inequality, the lower bound (-5) is greater than the upper bound (-11), which means there are no real numbers that satisfy this inequality. Therefore, inequality (a) is not satisfied by any real number x.
(b) -8 < x ≤ -7
In this inequality, the lower bound (-8) is less than the upper bound (-7), so there are real numbers that satisfy this inequality.
(c) 0 < x ≤ 4
In this inequality, the lower bound (0) is less than the upper bound (4), so there are real numbers that satisfy this inequality.
(d) -2 < x ≤ 6
In this inequality, the lower bound (-2) is less than the upper bound (6), so there are real numbers that satisfy this inequality.
Therefore, the inequality (a) -5 < x ≤ -11 is the one that is not satisfied by any real number x.