Solve the linear inequality $2x - 7 < -3x + 3$.

1. Problem Description

Solve the linear inequality $2x - 7 < -3x + 3$.

2. Solution Steps

We want to isolate $x$ on one side of the inequality.

First, add $3x$ to both sides of the inequality:

$2x - 7 + 3x < -3x + 3 + 3x$

$5x - 7 < 3$

Next, add $7$ to both sides of the inequality:

$5x - 7 + 7 < 3 + 7$

$5x < 10$

Finally, divide both sides of the inequality by $5$:

$\frac{5x}{5} < \frac{10}{5}$

$x < 2$

3. Final Answer

$x < 2$