### Video Transcript

The formula πΈ equals π plus three π plus πΏ over seven is often used by teachers to compute the estimated time needed by students to complete homework, πΈ, where π the shortest completion time, πΏ the longest, and π the most likely. Which of the following correctly gives πΏ in terms of πΈ, π, and π? A) πΏ equals seven πΈ minus π minus three π. B) πΏ equals π plus three π minus πΈ over seven. C) πΏ equals negative seven πΈ plus π plus three π. Or D) πΏ equals π plus three π plus πΈ over seven.

Instead of looking through the answer choices and trying to select which one is correct, the better option is to solve for πΏ ourselves and then line that up with one of the four answer choices. Weβre trying to get πΏ by itself. And to do that, weβll have to get rid of this fraction. So, we multiply both sides of the equation by seven over one. On the right, the sevens cancel out. And youβre left with π plus three π plus πΏ.

Seven over one times πΈ equals seven πΈ. From there, we subtract π from both sides. The πs on the right cancel out. So, we have seven πΈ minus π equals three π plus πΏ. And then, we subtract three π from both sides. On the right, the three πs cancel out. And we have seven πΈ minus π minus three π equals πΏ. If we flip that around, πΏ equals seven πΈ minus π minus three π, which is option A out of the answer choices.