Question

How do you solve `abs[5x -3] = -7x` and find any extraneous solutions?

Answer 1

`-3/2`

Explanation:

`|5x-3|=-7x > 0`. So, `x < 0.`

And so, the given equation for x < 0 becomes

`3-5x=-7x`, giving `x = -3/2`

See the graph. The only zero of

`y = |5x-3|+7x` is `x = -3/2`..

graph{|5x-3|+7x [-1.5, 1.5, -5, 5]}