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