Chapter 1.3, Problem 26E

To determine

To describe and correct the error.

Answer to Problem 26E

The correct solution is $c=\frac{5}{4}$ .

Explanation of Solution

Given information:

The equation is $6\left(2y+6\right)=4\left(9+3y\right)$ .

Calculation:

The error is in the last step, because

If the both sides are equal of an equation.

Then there are infinitely many solutions.

But the given solution is, the equation no solution.

This is the error in the given solution.

And the correct solution is,

  $\begin{array}{c}6\left(2y+6\right)=4\left(9+3y\right)\\ 12y+36=36+12y\end{array}$

Subtract 36 from both sides,

  $\begin{array}{c}12y+36-36=-36+36+12y\\ 12y=12y\end{array}$

Subtract $12y$ from both sides,

  $\begin{array}{c}12y-12y=12y-12y\\ 0=0\end{array}$

The both sides are equal.

So, there are infinitely many solutions.