# How do you solve #|8r+1|=3r# and find any extraneous solutions?

##### 1 Answer

There are no valid solutions to the given equation.

#### Explanation:

If

then

Note that neither of these solutions an be valid

since the left side must be positive and these solutions cause the right side to be negative.

However, we can check each possible solution explicitly:

[1]

[2]

Here is the graph of

graph{abs(8x+1) [-1.107, 1.594, -0.085, 1.265]}

and here is the graph of

graph{3x [-0.6154, 1.2815, -0.3, 0.6484]}

Notice the lines for these two expressions have no points in common. (Sorry I can't remember how to get both of these on the same graph and I'm not using my normal computer with s/w to do these better).