Question

Which Value is not a possible solution to the given inequality -|x+3|+2<-12

Answer 1

To solve the inequality -|x+3|+2<-12, we consider two cases for the absolute value: when x+3 is positive and when it is negative. After solving both cases, we find that all numbers less than -17 and all numbers greater than 11 satisfy the inequality. Any number between -17 and 11 is not a valid solution.

Step-by-step explanation:

The question involves solving an inequality which is a mathematical expression that compares two values and shows if one value is less than, greater than, or equal to another value. The inequality to solve here is -|x+3|+2<-12. This inequality features an absolute value, which means we need to consider two cases based on whether the expression inside the absolute value is positive or negative.

First, let's isolate the absolute value by subtracting 2 from both sides of the inequality:

-|x+3| < -14

Now we consider the two cases for the absolute value:

1. If x+3 is positive or zero, we have -|x+3| which simplifies to -(x+3). Thus the inequality becomes -(x+3) < -14, which simplifies to x+3 > 14 after multiplying both sides by -1 (and reversing the inequality sign).
2. If x+3 is negative, we have -|x+3| which is the same as x+3. Thus the inequality becomes x+3 < -14.

Solving both cases gives us:

1. x > 11
2. x < -17

Therefore, the values for x that satisfy the inequality are all the numbers less than -17 and all the numbers greater than 11. Any number between -17 and 11 is not a solution for the inequality.