Final answer:
The inequality -5/4(3x + 4) < 6 - 3x simplifies to x > -44/3 when solved step by step, starting with distribution and moving to isolating the variable x.
Step-by-step explanation:
To solve the inequality -5/4(3x + 4) < 6 - 3x, we first distribute the -5/4 across the parentheses:
- First, multiply -5/4 by 3x to get -15x/4.
- Then multiply -5/4 by 4 to get -5.
So we have -15x/4 - 5 < 6 - 3x.
Next, we add 15x/4 to both sides to get -5 < 6 + 15x/4 - 3x. Since 3x is the same as 12x/4, we can combine like terms on the right:
-5 < 6 + 3x/4
Now, we subtract 6 from both sides:
-11 < 3x/4
Finally, we multiply both sides by 4/3 to isolate x and obtain:
x > -44/3
Therefore, the solution to the inequality is x > -44/3.