Let's go through the steps you've outlined and solve for \( x \).
Starting with the equations:
- \( y = 4x - 5 \)
- \( x = -6y + 20 \)
We substitute \( y \) in the second equation:
\[ x = -6(4x - 5) + 20 \]
Next, distribute the -6:
\[ x = -24x + 30 + 20 \]
Combine the constants on the right side:
\[ x = -24x + 50 \]
Now, we'll add \( 24x \) to both sides to combine \( x \):
\[ x + 24x = 50 \]
This simplifies to:
\[ 25x = 50 \]
Now, divide both sides by 25:
\[ x = \frac{50}{25} \]
\[ x = 2 \]
Thus, the value of \( x \) is \( 2 \).