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3 years ago

What is the solution of |2x + 3| = 3x + 5?

Mathematics

2 answers:

Elanso [62]3 years ago

5 0

Answer:

$x=-\frac{8}{5}$

Step-by-step explanation:

The given absolute value equation is

$|2x+3|=3x+5$

This implies that;

$-(2x+3)=3x+5\:or\:2x+3=3x+5$

$-2x-3=3x+5\:or\:2x+3=3x+5$

Group similar terms in both equations;

$-2x-3x=5+3\:or\:2x-3x=5-3$

$-5x=8\:or\:-x=-2$

$x=-\frac{8}{5}\:or\:x=2$

CHECK

$|2(2)+3|=3(2)+5$

$|4+3|=6+5$

$7=11$ .

This false. Hence x=2 is an extraneous solution.

When $x=-\frac{8}{5}$

$|2(-\frac{8}{5})+3|=3(-\frac{8}{5})+5$

$|-\frac{16}{5}+3|=(-\frac{24}{5})+5$

$|-\frac{1}{5}|=\frac{1}{5}$

$\frac{1}{5}=\frac{1}{5}$

This statement is true

tekilochka [14]3 years ago

4 0

<h2>Answer:</h2>

<u>The right answer is </u><u>x = -8/5</u>

<h2>Step-by-step explanation:</h2>

See the attached figure

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I've attached a plot of the intersection (highlighted in red) between the parabolic cylinder (orange) and the hyperbolic paraboloid (blue).

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Some rewriting:

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This is a fairly standard integral (it even has its own Wiki page, if you're not familiar with the derivation):

$\displaystyle\int\sec^3z\,\mathrm dz=\frac12\sec z\tan z+\frac12\ln|\sec x+\tan x|+C$

So the arc length is

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4 years ago

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Step-by-step explanation:

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:) :) :)

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3 years ago

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Answer:

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If is typed like this 3-2x-3+3=

It will be

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