Inequality Solutions: Finding When -3x + 15 < 3x < 4x + 8 Holds True

To solve this problem effectively, we will proceed by solving each inequality separately:

• Step 1: Solve the inequality $-3x + 15 < 3x$.
• Add $3x$ to both sides to get: $15 < 6x$.
• Divide both sides by $6$ to solve for $x$: $x > \frac{15}{6}$, simplifying to $x > 2.5$.
• Step 2: Solve the second inequality $3x < 4x + 8$.
• Subtract $3x$ from both sides to isolate $x$: $0 < x + 8$.
• Subtract $8$ from both sides to find: $-8 < x$.
• Step 3: Find the overlap of the solutions.
• The solution to the inequalities $-8 < x$ and $x > 2.5$ is simply $x > 2.5$ since $x > 2.5$ is more restrictive.

Thus, the values of $x$ that satisfy the original compound inequality are those for which $x > 2.5$.

Therefore, the solution to the problem is $2.5 < x$.