Question

HELP!!!
Solve the equation. Check for extraneous solutions.
|4x+3|=9+2x

x= _________ or _________

Answer 1

\[\left| 4x+3 \right|=9+2x\]
\[4x+3=9+2x[1]\] or
\[4x+3=-(9+2x)[2]\]
\[[1]\]
\[4x-2x=9-3\]
\[2x=6\]
\[x=3\]
\[[2]\]
\[4x+3=-9-2x\]
\[6x=-12\]
\[x=-2\]
Therefore x=-2 or x=3

Make sure you check the solutions by testing them through substituting the values back into the original equation.
\[\left| 4(-2)+3 \right|=9+2(-2)\]
\[\left| -8+3 \right|=9-4\]
\[\left| -5 \right|=5\]
Get rid of the absolute value signs and you get a positive number no matter what.
Therefore 5=5 which means the solution "x=-2" is TRUE.

Answer 2

You can test the value x=3 back into the equation yourself to get to understand how to do it. Next time you see a similar question like this, you will know that you have to get the values and then afterwards, check ALL values to see whether they fit into that equation. If you substitute a value into both sides of the equation and you don't get the same result from both ends, you have an extraneous solution. That means you leave that solution out at the end of your working because it doesn't work out.