The Goal

Solve the following equation for x:

The Mistake

Find the algebra mistake:

Need a hint? Look carefully at the red part of the algebra:

The Correction

An Explanation

As "The Correction" shows, the attempted solution takes the long route to solving the equation, in addition to including three signs errors. First, adding (3/2)x to both sides is the way to remove the -(3/2)x from the right side. Second, add 4 to both sides to remove the -4 from the left side. Third, multiply by -2 to remove the factor -(1/2) on the left side.

To solve the equation more directly (and correctly), multiply out the 2(x-4) term and then combine x terms, while moving the non-x term to the right side. It does not help to move any of the x terms to the right!