Identify the solution and an extraneous solution.

Question

|5x+15|=10x

Answer 1

You can check for extraneous solutions without "plugin in".

or

When you look at the source equation, the absolute value is non-negative.

That mean the the solution has to satisfy inequality 10x>=0, or simply x>=0.

So you reject any negative solutions as extraneous

Answer 2

Remember that absolute functions can be described as

y = x for x≥ 0 and y = -x for x < 0.

Therefore there are 2 equations we need to solve

1. 5x+15 = 10x
2. -(5x+15) = 10x

Solving (1)

5x + 15 = 10x

-5x = -15

x = 3

Solving (2)

-(5x + 15) = 10x

5x + 15 = -10x

15x = -15

x = -1

However, when we plug -1 into 10x we get that x=-10 but when we plug -1 into |5x+15| we get that x=10. Therefore x=-1 is the extraneous solution

Answer 3