5-/x+4/<-3
To solve the inequality 5 - |x + 4| < -3, we can follow these steps:
Step 1: Remove the absolute value by considering two cases:
Case 1: x + 4 ≥ 0
If x + 4 ≥ 0, then |x + 4| = x + 4. So we can rewrite the inequality as 5 - (x + 4) < -3.
Simplifying, we get 1 - x < -3. Rearranging the terms, we have -x < -4. Dividing both sides by -1 and flipping the inequality sign due to dividing by a negative number, we get x > 4.
Case 2: x + 4 < 0
If x + 4 < 0, then |x + 4| = -(x + 4). So we can rewrite the inequality as 5 - (-(x + 4)) < -3.
Simplifying, we get 5 + x + 4 < -3. Combining like terms, we have x + 9 < -3. Rearranging the terms, we get x < -12.
Step 2: Combine the solutions:
Combining the results from both cases, we have x > 4 (for Case 1) and x < -12 (for Case 2). To find the intersection of these two solution sets, we need to find the values of x that satisfy both conditions. Since there is no overlap between x > 4 and x < -12, meaning they have no common values, there is no solution to the original inequality 5 - |x + 4| < -3.