Linear Equations in Disguise 04:05 minutes

Video Transcript

Transcript Linear Equations in Disguise

Clarissa loves to collect comics. She's always obsessed with finding the next hidden gem. One day while scouring the shelves, Clarissa totally flips out! Two special editions of “Miss Calculate" the adorably nerdy hero who helps people see the error of their ways! She goes up to the store owner, who tells her these editions are VERY valuable. Normally, Miss Calculate comics are labeled with linear equations. But these are labeled with NON-linear equations. Clarissa is skeptical, so she wants to check that they really are non-linear and not just linear equations in disguise! The label on the first comic is 'x' over 7 equals 14 over 98. This looks more like a proportion than a linear equation. But there IS a variable raised to the first power and the variables in linear equations are ALWAYS raised to the first power. Let’s rewrite this proportion by cross-multiplying. Take the numerator on the left side of the equation and multiply it by the denomintor on the right side. And take the denomintor on the left side of the equation and multiply it by the numerator on the right side. Now we have 98x equals 7 times 14 or 98x equals 98. We can simplify that even further by dividing both sides by 98.

Hold on: this special edition isn’t special at all! It's just the linear equation 'x' equals one! The comic store owner swears there must be some kind of mistake, but let's check out the second equation anyway. The quantity 'four minus x' over 9 equals the quantity 'three x plus two' over 36. This one looks more complicated, but the variables are all raised to the power of one so is it a linear equation or not? Let's simplify to check. Again we use cross multiplication. Take the numerator on the left side of the equation and multiply it by the denomintor on the right side. And take the denomintor on the left side of the equation and multiply it by the numerator on the right side then apply the distributive property to get 144 minus 36x equals 27x plus 18. Next, use opposite operations to isolate the variable. Start by subtracting 144 from both sides.

Then subtract 27x to both sides and finally divide both sides by negative 63 to get x' equals two? Are you kidding me? The second book is also labeled with an ordinary linear equation! So, to review: if you want to check if an equation is linear... First, simplify the equation. Then, isolate a variable. Finally, check to see if the variable or variables are all raised to the first power. Using this strategy, Clarissa knows that this comic book guy is definitely trying to rip her off! Looks like a job for Miss Calculate, defender of computational justice! Evildoers and renegade mathematicians, beware!