How do you solve for each of the variable #5L= 10L- 15D+ 5#?

1 Answer
Jul 30, 2015

Answer:

You take turns isolating them on one side of the equation.

Explanation:

Your starting equation looks like this

#5L = 10L - 15D + 5#

To solve this equation for #L#, get all the terms that contain this variable on one side of the equation.

In your case, you can do this by adding #-10L# to both sides of the equation

#5L - 10L = color(red)(cancel(color(black)(10L))) - color(red)(cancel(color(black)(10L))) - 15D + 5#

#-5L = -15D + 5#

Now divide both sides of the equation by #-5# to get

#(color(red)(cancel(color(black)(-5))) L)/color(red)(cancel(color(black)(-5))) = (-15D)/(-5) + 5/(-5)#

#L = color(green)(3D - 1)#

Now do the same for #D#. Notice that you can write

#5L = 10L + 5 - 15D#, so you could add #-10L - 5# to both sides of the equation to get

#5L - 10L - 5 = color(red)(cancel(color(black)(-10L - 5))) + color(red)(cancel(color(black)(10L + 5))) - 15D#

This is equivalent to

#-15D = -5L - 5#

Finally, divide both sides of the equation by #-15# to get

#(color(red)(cancel(color(black)(-15)))D)/color(red)(cancel(color(black)(-15))) = (-5L)/(-15) - 5/(-15)#

#D = 1/3L + 1/3#, or

#D = color(green)(1/3(L+1))#