Solve [2 - |2 - x|] / 3 = 1 / 5

[chrisw]

Solve the following:

. . .[2 - |2 - x|] / 3 = 1 / 5

I was thinking that I would cross multiply, but then it looked like:

. . .10 - |10 - 5x| = 3

If this is right, then what would I do with that negative in front of the absolute value? Should I distrubute?
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Edited by stapel -- Reason for edit: fixing formatting

 

[stapel]

Try getting the absolute-value bit by itself:

. . . . .\(\displaystyle \L \frac{2\, -\, |2\, -\, x|}{3}\, =\, \frac{1}{5}\)

Cross-multiplying is fine:

. . . . .\(\displaystyle \L 5\left(2\, -\, |2\, -\, x|\right)\, =\, 3(1)\)

. . . . .\(\displaystyle \L 10\, -\, 5|2\, -\, x|\, =\, 3\)

Now get the absolute-value part alone:

. . . . .\(\displaystyle \L 10\, -\, 3\, =\, 5|2\, -\, x|\)

. . . . .\(\displaystyle \L 7\, =\, 5|2\, -\, x|\)

. . . . .\(\displaystyle \L \frac{7}{5}\, =\, |2\, -\, x|\)

Then split it apart and handle in the usual manner:

. . . . .\(\displaystyle \L 2\, -\, x\, =\, \frac{7}{5}\, \mbox{ or }\, 2\, -\, x\, =\, -\frac{7}{5}\)

Solve in the usual way.

Eliz.

 

[chrisw]

Thank you