Tools for Solving Variable on Both Sides of an Equation
[One speaker]
[Video opens to a white screen with a yellow title reading “Tools for solving for a Variable on Both Sides of the Equation.” Also displayed is the same text, smaller, underlined, and in blue, above the title.]
Female Speaker: Welcome, this video goes over the tools you can use to solve for a variable when that variable is on both sides of the equation.
[New slide titled “Tools for Solving for a Variable on Both sides of the Equation. Listed are the points:
The narrator will write examples next to each point as she is discussing it.]
Here’s a list of some of the tools that can help you when you’re trying to solve for a variable that appears on both sides of an equation. One of the first things to look at is if there are like terms and you want to combine all the like terms. Like terms are things like two x and five x [Writes “2x” and “5x”]. Each term has the same variable, and so they are like terms, they are similar to each other. Another example would just be the numbers four and twenty two point six [Erases the previous text and writes “4” and “22.6”]. Both of these are numbers, they don’t have a variable, and so they alike. Other terms like three x and four x squared are not alike because they have different variables [Erases the previous text and writes “3x” and “4x2,” then a large red x goes through them]. Three x has x as a variable, and four x squared has x squared as a variable. So they are not terms that you could combine.
Another tool is to use the distributive property of multiplication. For example if you see something like three times one plus x [Erases the previous text and writes “3(1+x)”], you can distribute this to equal three times one plus three x, or three times x [writes “=3(1)=3x”]. So the distributive property multiplies to everything within the parenthesis. [Draws arrows from the first “3” to both the “1” and “x” within the parenthesis]
Another tool is to add the additive inverse of terms to both sides of the equation. For example, three x plus one equals five [Erases the previous text and writes “3x+1=5”]. In order to get the one to the other side of the equation, we add its inverse. So we add negative one to both sides [Writes “+-1” under the “+1” and the “5”, ad crosses out the “+1” and “+-1”]. This essentially removes one from the left-hand side, because one plus a negative one equals zero. And we’re left with three x on the left-hand side and four on the right-hand side. Five plus a negative one is four [Writes “3x=4” under all other text].
Another tool we can use is to multiply both sides by the multiplicative inverse. An example of this could be three x equals two [Erases the previous text and writes “3x=2”]. In order to isolate the x and change the coefficient of three into a one, we multiply both sides by the inverse of three, or one third [Writes parenthesis around the “3x” and writes ⅓ to the left of it]. Anything we do to the left-hand side we do to the right-hand side as well, so we multiply by one third on the right-hand side [Writes parenthesis around the “2” and writes ⅓ to the right of it]. And three times one third equals one. One x equals two divided by three [Writes under all other text ”1x=⅔”]. One x is the same as x, so x itself equals two divided by three. [Writes “x=⅔” under all other text, then erases it all.]
So, when trying to solve for a variable that appears on both sides of the equation, these are some of the tools that you can use to help you.
[End of Video.]