To solve the equation \( 10x - 1 = 7x + 26 \), follow these steps:
-
Rearrange the equation to get all terms involving \( x \) on one side and constant terms on the other side. Subtract \( 7x \) from both sides:
\[ 10x - 7x - 1 = 26 \]
This simplifies to:
\[ 3x - 1 = 26 \]
-
Add 1 to both sides to isolate the term with \( x \):
\[ 3x - 1 + 1 = 26 + 1 \]
This simplifies to:
\[ 3x = 27 \]
-
Divide both sides by 3 to solve for \( x \):
\[ x = \frac{27}{3} = 9 \]
So, the solution is:
\[ \boxed{9} \]