Final answer:
The solution to the inequality -5/2(3x+4)<6-3x is x < 4/7.
Step-by-step explanation:
To solve the given inequality, we'll follow the steps required to isolate the variable x.
First, distribute the -5/2 on the left side of the inequality:
-15x/2 - 10 < 6 - 3x
Next, add 3x to both sides to get the x terms on one side of the inequality:
-15x/2 - 10 + 3x < 6
Combine like terms by finding a common denominator:
(-15x + 6x - 20) / 2 < 6
Now, simplify the left side:
(-9x - 20) / 2 < 6
Multiply both sides by 2 to eliminate the fraction:
-9x - 20 < 12
Add 20 to both sides:
-9x < 32
Finally, divide both sides by -9, remembering to reverse the inequality because we're dividing by a negative number:
x > -32/9
So, the solution to the inequality is x < 4/7.