To solve the equation [tex]\(4x + 24x - 2 = 7(4x + 2)\)[/tex], let's follow a detailed, step-by-step process:
1. Combine like terms on the left side of the equation:
[tex]\[
4x + 24x - 2 = 28x - 2
\][/tex]
2. Distribute on the right side of the equation:
[tex]\[
7(4x + 2) = 28x + 14
\][/tex]
3. Substitute the simplified left and right sides back into the equation:
[tex]\[
28x - 2 = 28x + 14
\][/tex]
4. Next, we try to isolate [tex]\(x\)[/tex]. Subtract [tex]\(28x\)[/tex] from both sides:
[tex]\[
28x - 2 - 28x = 28x + 14 - 28x
\][/tex]
Simplifying this, we get:
[tex]\[
-2 = 14
\][/tex]
5. Notice that the equation [tex]\(-2 = 14\)[/tex] is a contradiction. This means no value of [tex]\(x\)[/tex] will satisfy the equation.
Since we have a contradiction and no value of [tex]\(x\)[/tex] satisfies the equation, the correct choice is:
[tex]\[
\boxed{\text{C. The equation has no solution.}}
\][/tex]
To summarize, your friend likely made an error in simplifying or solving the equation and incorrectly determined that [tex]\(x = 16\)[/tex]. The correct conclusion is that the given equation has no solution.
