Question

Solve each equation. Check for extraneous solutions.
|3x+5|=5x+2

Answer 1

Use the definition of absolute value.

Either (3x+5)=5x+2 or -(3x+5)=5x+2

Solving the first equation gives 2x=3 or x=3/2

Solving the second equation gives 8x=-7 or x=-7/8.

Checking both answers in the original equations, it looks to me like -7/8 is extraneous, since the left side would be + and the right side would be negative.

So x=3/2.

Answer 2

Verifying it graphically confirmed that there is only one solution, by the way.