Solve the equation and check for extraneous equations.
9|9-8x|=2x+3
Help me please I am stuck on this question.

Question

Solve the equation and check for extraneous equations.
9|9-8x|=2x+3
Help me please I am stuck on this question.

dape · Answer

The absolute value can be written as $|x|=x$ when $x≥0$ and $|x|=-x$ when $x<0$. So you can split your equation in two by imposing conditions on each equation.

anonymous · Answer

So what would be the answer? Im confused.

dape · Answer

So when $9-8x≥0\Leftrightarrow x≤\frac{9}{8}$ we have $|9-8x|=9-8x$ and the other case, namely $x>\frac{9}{8}$ we have $|9-8x|=-(9-8x)=8x-9$. Put this in and solve both equations.

dape · Answer

Then check that the solutions to those equations really satisfy the inequalities, otherwise you have found a extraneous solution (a solution that you got from these sub-problems but wasn't a solution to the original problem).

anonymous · Answer

Im still confused all I really wanted was the answer

dape · Answer

Well then you won't need this site, try here: http://www.wolframalpha.com/input/?i=solve+9%7C9-8x%7C%3D2x%2B3