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3 years ago

8

Solve absolute value equation. Check for extraneous solution. |2x-3|=2x-1. Post it into the drop box for the unit 2 review.

1 answer:

polet [3.4K]3 years ago

6 0

let's keep in mind that, an absolute value expression is in effect a piecewise one, since it has a ± versions of it.

$\bf |2x-3|=2x-1\implies \begin{cases}+(2x-3)=2x-1\\-(2x-3)=2x-1\end{cases}\\\\[-0.35em]~\dotfill\\\\+(2x-3)=2x-1\implies 2x-3=2x-1\implies -3 \ne -1\impliedby extraneous\\\\[-0.35em]~\dotfill\\\\-(2x-3)=2x-1\implies 2x-3=-2x+1\implies 4x=4\\\\\\x=\cfrac{4}{4}\implies x=1$

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Answer:

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Step-by-step explanation:

Given

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See attachment for illustration

Required

Find x

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$\triangle ADE \sim \triangle ACB$ --- similar triangles

So, we have the following equivalent ratios

$AE:DE = AB:CB$

Where:

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Express as fraction

$\frac{20}{x/2} = \frac{x + 34}{1775}$

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Cross multiply

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$x^2 + 34x = 71000$

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x can't be negative;

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$x = 250$

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