To find the value of \(\( x \)\), we need to set the given expressions equal to each other and solve for \(\( x \)\). The expressions are \(\( 6x - 1 \)\) and \(\( 8x - 43 \)\).
Let's set them equal to each other:
\(\[ 6x - 1 = 8x - 43 \]\)
Now, we want to solve for \(\( x \)\). To do this, follow these steps:
1. Move all terms involving \(\( x \)\) to one side by subtracting \(\( 6x \)\) from both sides:
\(\[ 6x - 1 - 6x = 8x - 43 - 6x \]\)
This simplifies to:
\(\[ -1 = 2x - 43 \]\)
2. Isolate the term with \(\( x \)\) by adding 43 to both sides:
\(\[ -1 + 43 = 2x - 43 + 43 \]\)
This simplifies to:
\(\[ 42 = 2x \]\)
3. Solve for \(\( x \)\) by dividing both sides by 2:
\(\[ \frac{42}{2} = \frac{2x}{2} \]\)
This simplifies to:
\(\[ 21 = x \]\)
Therefore, the value of \(\( x \)\) is \(\( 21 \)\).
\(\[
\boxed{21}
\]\)
