To solve the equation \( 26 = 9x + 2 - 5x \), we can start by simplifying the right side.
- Combine the terms involving \( x \):
\[ 9x - 5x = 4x \]
So, the equation simplifies to:
\[ 26 = 4x + 2 \]
- Next, we move the constant term (2) to the left side by subtracting 2 from both sides of the equation:
\[ 26 - 2 = 4x \]
This simplifies to:
\[ 24 = 4x \]
- Now, we can solve for \( x \) by dividing both sides by 4:
\[ x = \frac{24}{4} = 6 \]
So, the solution is \( x = 6 \).
Check the solution:
Substituting \( x = 6 \) back into the original equation:
\[ 26 = 9(6) + 2 - 5(6) \]
Calculating the right side:
\[ 9(6) = 54 \] \[ 5(6) = 30 \]
So, substituting these values gives:
\[ 26 = 54 + 2 - 30 \] \[ 26 = 56 - 30 \] \[ 26 = 26 \]
Since both sides of the equation are equal, the solution \( x = 6 \) is confirmed to be correct.
Final Answer:
\[ x = 6 \]