<, >, ≤, ≥ and Graphing Inequalities
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View: Lyric Explanation
Inequalities are made up of two expressions
Where we isolate the variable with inverse operations
In a “10 is less than 2x” formation
Divide the 2 by both sides to find the 5, X relation
Open circle over 5, arrow to the right
X is greater than five
Chorus:
Inequality is graphed on the number line
Like circle open to the left
Or circle closed to the right - uh huh
X is less than 5, open circle, left along that line
Or greater than or equal to 9
A closed circle and an arrow to the right
Here’s a 4 symbol range design
Inequalities, familiar, those two expressions
Negative 3x plus 2 is greater than or equal to 11
Isolate the variable with inverse operations
But when you’re dividing by a negative
The symbol turns direction
A closed circle, arrow to the left
X less than or equal to negative 3 is the best
Open to the left, greater than
Open to the right, less than
Open to the left, bar, greater than or equal to
Open to the right, bar, less than or equal to
Equations with a Variable on Both Sides
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View: Lyric Explanation
Express 5 times the quantity 3x minus 2
Let’s pass out, unpack, or distribute
Multiply that 5 by both terms in parenthesis
Say, 15x plus negative 10, can’t you?
Let’s get those negatives done
Just think: negative sum
A negative sign before the quantity
An understood “1″
Chorus:
The same variable on both sides of the equation
Distribute quantities first, in each expression
Combine like terms ’til each side confirms
And says: “We’re pretty sure this side is simplified”
Isolate the variable, in conclusion
We use the inverse and inverse operations
Subtract or add from both sides
Then multiply or divide
And say: “Here’s some isolation, simplified”
Express 2 times the quantity 2x plus 5
minus the quantity x minus 9
4x plus 10 minus x plus 9
Hey, the like terms are gonna combine
I simplify the integers
By adding the 9 and the 10
Now combine the one’s with variables
It’s 3x + 19 man!
If the x is all real numbers
Then it will cancel and disappear
Yea we’ll be left with the true equation
6 equals 6 is my favorite cheer
Or it could lead to no solution
3 equals 22
No x works here…
Yea, no x here
I use the inverse operations
To get the variable to isolate
13 minus 2x equals 3x plus 8
Subtract the 8 from every side
Leaving 3x on the right
5 minus 2x equals 3x this time
Add 2x to both sides
5x now equals that 5
Now all we do is divide
x=1, simplified