Final answer:
To solve the compound inequality, we can solve each inequality separately and then combine the solutions. The solution to the compound inequality 4-7x>-3 or 5(x-3)+8>3 is x<1 or x>2.
Step-by-step explanation:
To solve the compound inequality 4-7x>-3 or 5(x-3)+8>3, we can solve each inequality separately and then combine the solutions.
For the first inequality, 4-7x>-3, we can subtract 4 from both sides to get -7x>-7. Then, dividing by -7 (and remembering to flip the inequality sign since we're dividing by a negative number), we find that x<1.
For the second inequality, 5(x-3)+8>3, we can start by distributing the 5, giving us 5x-15+8>3. Simplifying further, we have 5x-7>3. We can then add 7 to both sides to get 5x>10, and finally divide by 5 to find that x>2.
Therefore, the solution to the compound inequality is x<1 or x>2.