The problem asks us to solve the inequality $-5x+6 > -2x+9$ and identify the corresponding number line representation of the solution.

1. Problem Description

The problem asks us to solve the inequality $-5x+6 > -2x+9$ and identify the corresponding number line representation of the solution.

2. Solution Steps

First, we solve the inequality:

$-5x+6 > -2x+9$

Add $5x$ to both sides:

$6 > 3x + 9$

Subtract 9 from both sides:

$-3 > 3x$

Divide both sides by 3:

$-1 > x$

This is equivalent to $x < -1$.

Now we need to identify the number line that represents $x < -1$.

The number line should have an open circle at -1, since the inequality is strictly less than, and the arrow should point to the left, indicating values less than -

1.

3. Final Answer

The solution to the inequality is $x < -1$. The number line representation has an open circle at -1 and the arrow pointing to the left.

The correct option is the first one.