Simple algebra question.

**Splint** · September 20th 2009, 06:20 AM

Please be understanding if this is a stupid question as I am making a comeback to algebra after 20 years of not using it.

The following appears in my text book...
$\frac{x}{3\sqrt(100^2+x^2)}=\frac{1}{5}$
the next line is....
$5x=3\sqrt(100^2+x^2)$
it is the $5x$ which bothers me, I would have thought to multiply both sides by $3\sqrt(100^2+x^2)$ then divide both sides by $\frac{1}{5}$ which would in my mind result in $\frac{x}{5}=3\sqrt(100^2+x^2)$
Have I missed the point here?

Splint

**aidan** · September 20th 2009, 06:34 AM

Originally Posted by Splint

Please be understanding if this is a stupid question as I am making a comeback to algebra after 20 years of not using it.

The following appears in my text book...
$\frac{x}{3\sqrt(100^2+x^2)}=\frac{1}{5}$
the next line is....
$5x=3\sqrt(100^2+x^2)$
it is the $5x$ which bothers me, I would have thought to multiply both sides by $3\sqrt(100^2+x^2)$ then divide both sides by $\frac{1}{5}$ which would in my mind result in $\frac{x}{5}=3\sqrt(100^2+x^2)$
Have I missed the point here?

Splint

Division by $\dfrac{1}{5}$ is equivalent to multiplication by 5.
You have divided the RHS by $\dfrac{1}{5}$ ,
but
you have divided the LHS by 5.

You multiplied through with the square root part and had no problem -- follow that by multiply both sides by 5.

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