Question

1. check for reasonableness your friend solved the equation 4x + 12x - 6 = 4(4x + 7) and got x = 34. what error did your friend make? what is the correct solution? 4x + 12x - 6 = 4(4x + 7) 16x - 6 = 16x + 28 16x - 16x - 6 = 16x - 16x + 28 x - 6 = 28 x - 6 + 6 = 28 + 6 x = 34

Explanation:

Step1: Simplify both sides of the equation

Combine like - terms on the left - hand side: $4x + 12x-6=16x - 6$. Expand the right - hand side: $4(4x + 7)=16x+28$. So the equation becomes $16x - 6=16x + 28$.

Step2: Analyze the error

Your friend made an error when subtracting $16x$ from both sides. When you subtract $16x$ from both sides of the equation $16x - 6=16x + 28$, you get $16x-16x - 6=16x-16x + 28$, which simplifies to $-6 = 28$. This is a contradiction, meaning there is no solution for $x$. The $x$ terms cancel out completely, and the remaining constants are not equal.

Answer:

The error is that your friend wrongly thought that after subtracting $16x$ from both sides, the $x$ on the left - hand side would remain. The correct solution is that there is no solution for the equation.