Question

Describe and correct the error in solving the equation for x.

Answer 1

`(10 +3b)/(a) =x`

Explanation:

By manipulating equations, we can solve for different variables.

Error

The error in the equation is in the factoring. In the second line, the x is factored out of the expression; however, this cannot be factored. Factoring is like dividing. When you factor x out you divide the terms by x. Since there is not an x in 3b, x cannot be factored out.

A correct version of factoring looks like:

• ax - 3bx + 2cx = x (a - 3b + 2c)

Correction

Now, we can go back to the beginning and solve for x correctly using the properties of equality. First, rewrite the equation.

• 10 = ax - 3b

Then, add 3b to both sides.

• 10 + 3b = ax

Finally, divide by a.

• 
  `(10 +3b)/(a) =x`

This is the final, correct equation solved for x.