The image you uploaded seems to show a geometry problem involving angles. The task is to find the value of $x$, given two angle expressions, $\alpha = 9(x + 1)$ and $\beta = -x + 19$. The two angles are presumably on a straight line at the intersection point.

The relationship between angles on a straight line is that they must add up to $180^\circ$. Therefore, we can set up the equation:

$\alpha + \beta = 180$

Substituting the expressions for $\alpha$ and $\beta$:

$9(x + 1) + (-x + 19) = 180$

Now, we can solve this equation to find the value of $x$. Let's simplify and solve:

$9(x + 1) - x + 19 = 180$

Distribute the 9:

$9x + 9 - x + 19 = 180$

Combine like terms:

$8x + 28 = 180$

Subtract 28 from both sides:

$8x = 152$

Now, divide by 8:

$x = 19$

Thus, the value of $x$ is $19$.

Would you like further details or have any questions? Here are some related topics you might find interesting:

1. What are complementary and supplementary angles?
2. How can you solve for unknown variables in geometric equations?
3. The significance of angles in parallel lines and transversals.
4. What is the concept of vertical angles and their properties?
5. How do you apply the angle sum property in various polygons?

Tip: Always double-check that the sum of angles on a straight line equals 180° when working with angle problems!