The Goal

Solve the following equation for x:

The Mistake

Find the algebra mistake:

(Roll the mouse over the algebra to see a hint in red)

The Correction

(Roll the mouse over the area above to see the correction in blue)

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!