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

Jan 7, 2017

$- \frac{3}{2}$

Explanation:

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

And so, the given equation for x < 0 becomes

$3 - 5 x = - 7 x$, giving $x = - \frac{3}{2}$

See the graph. The only zero of

$y = | 5 x - 3 | + 7 x$ is $x = - \frac{3}{2}$..

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