Final answer:
To solve the inequality, distribute and combine like terms. Divide by -3.5 to isolate x. The solution is x < -6.71.
Step-by-step explanation:
To solve the inequality, we need to simplify the expression first. Distribute the -1.5 and -2.5 to the terms inside the parentheses:
-1.5(4x + 1) > 24.5 - 2.5(x + 1)
-6x - 1.5 > 24.5 - 2.5x - 2.5
Combine like terms:
-6x - 1.5 > 22 - 2.5x
Add 2.5x to both sides:
-6x + 2.5x - 1.5 > 22
-3.5x - 1.5 > 22
Add 1.5 to both sides:
-3.5x > 23.5
Divide by -3.5 (remember to switch the inequality sign when dividing by a negative number):
x < -23.5/3.5
Simplify the fraction:
x < -6.71
The solution set to the inequality is (-infinity, -6.71).