5-|x+4| ≤ -3
≤ is less than or equal to sign
Thanks!
To solve the inequality 5-|x+4| ≤ -3, we can follow these steps:
Step 1: Remove the absolute value by considering both cases.
Case 1: If x+4 < 0, then |x+4| = -(x+4)
In this case, the inequality becomes 5 - (-(x+4)) ≤ -3.
Simplifying this, we get 5 + x + 4 ≤ -3.
Combining like terms, we have x + 9 ≤ -3.
Now, subtracting 9 from both sides, we get x ≤ -12.
Case 2: If x+4 ≥ 0, then |x+4| = x+4.
In this case, the inequality becomes 5 - (x+4) ≤ -3.
Simplifying this, we get 5 - x - 4 ≤ -3.
Combining like terms, we have 1 - x ≤ -3.
Now, adding x to both sides and subtracting 1 from both sides, we get -x ≤ -4.
Multiplying both sides by -1 (and reversing the inequality), we have x ≥ 4.
Step 2: Combine the results from both cases.
In case 1, we found x ≤ -12.
In case 2, we found x ≥ 4.
Since these inequalities have no intersection, the solution is x ≤ -12 or x ≥ 4.