We are asked to solve the inequality $2x - 10 \leq 7x - 9$ for $x$.

1. Problem Description

We are asked to solve the inequality $2x - 10 \leq 7x - 9$ for $x$.

2. Solution Steps

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

First, we subtract $2x$ from both sides of the inequality:

$2x - 10 - 2x \leq 7x - 9 - 2x$

$-10 \leq 5x - 9$

Next, we add $9$ to both sides of the inequality:

$-10 + 9 \leq 5x - 9 + 9$

$-1 \leq 5x$

Now, we divide both sides of the inequality by $5$:

$\frac{-1}{5} \leq \frac{5x}{5}$

$-\frac{1}{5} \leq x$

This can also be written as:

$x \geq -\frac{1}{5}$

3. Final Answer

$x \geq -\frac{1}{5}$