Solve the inequality $6x + 13 < 5(2x - 3)$ for $x$.

1. Problem Description

Solve the inequality $6x + 13 < 5(2x - 3)$ for $x$.

2. Solution Steps

First, we distribute the 5 on the right side of the inequality:

$6x + 13 < 5(2x) - 5(3)$

$6x + 13 < 10x - 15$

Next, we want to isolate the x terms on one side and the constants on the other. We can subtract $6x$ from both sides:

$6x + 13 - 6x < 10x - 15 - 6x$

$13 < 4x - 15$

Then, we add 15 to both sides:

$13 + 15 < 4x - 15 + 15$

$28 < 4x$

Finally, we divide both sides by 4:

$\frac{28}{4} < \frac{4x}{4}$

$7 < x$

This can be rewritten as $x > 7$.

3. Final Answer

$x > 7$