4-3|m+2|>-14
To solve the inequality 4 - 3|m + 2| > -14, we can break it down into two cases.
Case 1: m + 2 ≥ 0
In this case, the absolute value |m + 2| is equal to m + 2. We can rewrite the inequality as:
4 - 3(m + 2) > -14
To solve for m, we can follow these steps:
1. Distribute -3 to both terms inside the parentheses:
4 - 3m - 6 > -14
2. Combine like terms:
-3m - 2 > -14
3. Add 2 to both sides to isolate -3m:
-3m > -12
4. Divide both sides by -3, remembering to reverse the inequality since we're dividing by a negative number:
m < 4
So, for this case, the solution is m < 4.
Case 2: m + 2 < 0
In this case, the absolute value |m + 2| is equal to -(m + 2). We can rewrite the inequality as:
4 - 3(-(m + 2)) > -14
To solve for m, we can follow these steps:
1. Distribute -3 to both terms inside the parentheses:
4 + 3m + 6 > -14
2. Combine like terms:
3m + 10 > -14
3. Subtract 10 from both sides:
3m > -24
4. Divide both sides by 3:
m > -8
So, for this case, the solution is m > -8.
Combining the two cases, we get the solution to the inequality 4 - 3|m + 2| > -14 as:
m < 4 or m > -8.