Answer: the solution to the inequality -3|x+4| < 2x+9 is x > -21/5 and x < -3.
Step-by-step explanation:To solve the inequality -3|x+4| < 2x+9, we need to follow these steps:
1. Break the inequality into two separate cases:
a) When the expression inside the absolute value (x+4) is non-negative:
In this case, we can remove the absolute value signs.
b) When the expression inside the absolute value (x+4) is negative:
In this case, we need to multiply the absolute value expression by -1 and reverse the inequality sign.
2. Solve the inequality for each case:
a) When x+4 is non-negative:
-3(x+4) < 2x+9
Simplify the equation by distributing -3:
-3x - 12 < 2x + 9
Combine like terms:
-5x - 12 < 9
Add 12 to both sides:
-5x < 21
Divide both sides by -5 (since we are dividing by a negative number, the inequality sign flips):
x > -21/5
b) When x+4 is negative:
-3(-(x+4)) < 2x + 9
Simplify the equation by distributing -3 and -1:
3x + 12 < 2x + 9
Subtract 2x from both sides:
x + 12 < 9
Subtract 12 from both sides:
x < -3
3. Combine the solutions from both cases:
The solutions are x > -21/5 and x < -3.
Therefore, the solution to the inequality -3|x+4| < 2x+9 is x > -21/5 and x < -3.