Let's build the equation counting how many x's and 1's are there on each side.
On the left hand side we have 5x's and 8 1's, for a total of 
On the left hand side we have 3x's and 10 1's, for a total of 
So, the equation we want to solve is
Subtract 3x from both sides:
Subtract 8 from both sides:
Divide both sides by 2:
Answer:
Step-by-step explanation:
2x2 + 8x - 3x - 12
2x2 + 5x - 12 is equivalent to the given expression
<em>x</em>/<em>r</em> + <em>x</em>/<em>w</em> + <em>x</em>/<em>t</em> = 1
<em>x</em> (1/<em>r</em> + 1/<em>w</em> + 1/<em>t</em>) = 1
<em>x</em> = 1 / (1/<em>r</em> + 1/<em>w</em> + 1/<em>t</em>)
To make the solution a bit cleaner, multiply through the numerator and denominator by the LCM of each fraction's denominator, <em>rwt</em> :
<em>x</em> = 1 / (1/<em>r</em> + 1/<em>w</em> + 1/<em>t</em>) • <em>rwt</em> / <em>rwt</em>
<em>x</em> = <em>rwt</em> / (<em>rwt</em>/<em>r</em> + <em>rwt</em>/<em>w</em> + <em>rwt</em>/<em>t</em>)
<em>x</em> = <em>rwt</em> / (<em>wt</em> + <em>rt</em> + <em>rw</em>)
Karl ate 5/6 of a small bag of popcorn .
