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

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Answer 1 · 2017-01-07T16:30:31

$- \frac{3}{2}$ $-3/2$

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

And so, the given equation for x < 0 becomes

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

See the graph. The only zero of

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

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

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