Question

Graph the solution to the following inequality: 5|2 + 11|< 25 < 10

a) No solution
b) x > 4
c) x < -4
d) -4 < x < 4

Answer 1

The provided inequality seems to have a typo and does not contain a variable 'x'. Assuming a corrected inequality 5|x + 2| < 25, the solution is -7 < x < 3 by considering the two cases for the absolute value. This solution is not listed among the provided options.

Step-by-step explanation:

To graph the solution to the inequality 5|2 + 11| < 25, we notice an apparent typographical error in the inequality expression, which does not contain a variable 'x'. However, assuming that the inequality should be 5|x + 2| < 25, we can find the solution by considering two cases depending on whether the expression inside the absolute value is positive or negative.

First Case (x + 2 >= 0):

1. 5|x + 2| = 5(x + 2)
2. 5x + 10 < 25
3. 5x < 15
4. x < 3

Second Case (x + 2 < 0):

1. 5|x + 2| = 5(-(x + 2))
2. 5(-x - 2) < 25
3. -5x - 10 < 25
4. -5x < 35
5. x > -7

Combining both cases, the solution is -7 < x < 3, which is not one of the provided options. Therefore, we would need further clarification on the initial inequality to determine the correct answer.