Sure! Let's solve the equation [tex]\(2x - 8 = 6 - 7x\)[/tex] step by step.
1. First, we want to combine like terms by getting all the terms involving [tex]\(x\)[/tex] on one side of the equation and constants on the other side. To do this, we can add [tex]\(7x\)[/tex] to both sides of the equation:
[tex]\[2x - 8 + 7x = 6 - 7x + 7x\][/tex]
2. Simplify the equation by combining like terms:
[tex]\[2x + 7x - 8 = 6\][/tex]
[tex]\[9x - 8 = 6\][/tex]
3. Next, we need to isolate the [tex]\(x\)[/tex] term. To do this, add 8 to both sides of the equation:
[tex]\[9x - 8 + 8 = 6 + 8\][/tex]
4. Simplify the equation:
[tex]\[9x = 14\][/tex]
5. To solve for [tex]\(x\)[/tex], divide both sides of the equation by 9:
[tex]\[x = \frac{14}{9}\][/tex]
Therefore, the solution to the equation [tex]\(2x - 8 = 6 - 7x\)[/tex] is [tex]\(x = \frac{14}{9}\)[/tex].
So the correct answer is:
[tex]\[
\boxed{\frac{14}{9}}
\][/tex]
