A 4-Step Guide to Solving Equations (Part 1)

Do you think that solving equations is hard? Would you believe that it doesn’t have to be? Want to learn an easier way how? Keep on reading to find out!

Jason Marshall, PhD,
June 21, 2013
Episode #158

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A 4-Step Guide to Solving Equations (Part 1)

Once upon a time, a group of seafaring pyramid builders who were the biggest rivals to our dynamic duo of ancient Egyptian pyramid builders—Knot Dude and his father Papa Knot—proclaimed that “Any rookie pyramid builder can construct pyramids with square bases, but only a true master can create pyramids with bases shaped like rectangles!”

These antagonistic scalawags even scoffed at Papa Knot’s favorite method for creating square bases. They said that using the Pythagorean Theorem to calculate the length of the diagonal across a square pyramid’s basebefore measuring it out was “too easy” since “the equation is almost solved for you. Just plug a and b into a^2 + b^2 = c^2, and you’re done!”

See also: Why Is Algebra Useful?

At one point, they even went so far as to issue Knot Dude a direct challenge, saying: “If we were to ask you to build a small rectangular pyramid with one side that’s 15 feet long and a diagonal that’s 17 feet long, could you figure out how long the shorter side would have to be? Or is that too much work for you?”

Pretty strong words, right? Could Knot Dude do it? Of course he could…he was the Knot Dude, after all. So how did he do it? What did it have to do with the golden rule for equation solving that we learned last time? And how can you use Knot Dude’s easy 4-step method for solving equations? Stay tuned because those are exactly the questions we’ll be answering today..

Recap: The Golden Rule

That which you do to one side of an equation, you must also do to the other.

Remember that rule? I hope so because, as we learned about last time, this golden rule of equation solving is going to be super important in all of your future equation solving endeavors. And it was super important for Knot Dude, too. He knew that he could solve his nemesis’ puzzle by somehow using a and c in the Pythagorean equation to solve for b. (If you don’t see why, I encourage you to stop for a minute and think about it!)

And not only that, the golden rule was also the key idea that helped Knot Dude discover his 4-step method for solving equations…exactly the method we’ll be learning over the next few weeks. Speaking of which, the first step of that method is…


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