Question

solve the equation. 8x - 2(x - 6) = 6(x + 1) + 7 select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution is \boxed{} (simplify your answer.) b. the solution is all real numbers. c. there is no solution.

Explanation:

Step1: Expand both sides

First, we expand the left - hand side and the right - hand side of the equation \(8x-2(x - 6)=6(x + 1)+7\).

For the left - hand side:
Using the distributive property \(a(b + c)=ab+ac\), we have \(8x-2(x - 6)=8x-(2x-12)=8x - 2x + 12=6x+12\)

For the right - hand side:
\(6(x + 1)+7=6x+6 + 7=6x+13\)

So the equation becomes \(6x + 12=6x+13\)

Step2: Subtract \(6x\) from both sides

Subtract \(6x\) from both sides of the equation \(6x + 12=6x+13\). We get \((6x-6x)+12=(6x - 6x)+13\), which simplifies to \(12 = 13\)

Since \(12
eq13\), this is a contradiction.

Answer:

C. There is no solution.