Final answer:
The solution to the inequality is x > -32/9.
Step-by-step explanation:
To solve the inequality -5/2(3x+4) < 6-3x, we need to simplify both sides of the inequality.
Let's start by distributing -5/2 to the expression inside the parentheses on the left side:
-5/2 * 3x - 5/2 * 4 < 6 - 3x
Next, multiply -5/2 by 3x and -5/2 by 4 to get:
-15/2x - 10 < 6 - 3x
To isolate the variable x, let's collect like terms. Add 3x to both sides of the inequality:
-15/2x + 3x - 10 < 6
Simplify the left side of the inequality:
-15/2x + 6/2x - 10 < 6
Combine like terms:
-9/2x - 10 < 6
Add 10 to both sides of the inequality:
-9/2x - 10 + 10 < 6 + 10
Simplify the right side of the inequality:
-9/2x < 16
To get rid of the fraction, multiply both sides of the inequality by -2/9 (the reciprocal of -9/2):
(-2/9)(-9/2x) > (-2/9)(16)
Simplify the left side of the inequality:
x > -32/9
Hence, the solution to the inequality is x > -32/9.