Unit 6
Equations & Inequalities
Equations & Inequalities
Intro:
An equation is like a balanced scale.
Whatever is on the right side of the equation is the same as whatever is on the right side of the equation.
Whatever is on the right side of the equation is the same as whatever is on the right side of the equation.
Consider the following balanced scale:
10 + 10 = 20
When we say two things are equal,
we are saying that everything that is true about 10 + 10
is also true about 20.
They are interchangeable.
That's why you could pay for something with two tens or a single twenty, and you are perfectly within your rights to do so.
Many times in algebra, we use a variable on one side of the equation.
x = 20
As you improve your algebra skills, the x will be hidden by more and more obstacles. Much of this unit is how to get rid of some obstacles around the variable.
Your job is to make sure the equation stays balanced.
Your job is to make sure the equation stays balanced.
Because if you don't keep the equation balanced...
...you no longer have an equation. You have an inequality. More on that in the next lesson.
Notebook:
Classwork & Homework:
Design a balanced scale to represent an equation.
Answers are below.
State Test Practice:
California Standards:
CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
CCSS.Math.Practice.MP4 Model with mathematics.
CCSS.Math.Practice.MP7 Look for and make use of structure.
CCSS.Math.Content.6.EE.A.4
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
CCSS.Math.Content.6.EE.B.6
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
CCSS.Math.Practice.MP4 Model with mathematics.
CCSS.Math.Practice.MP7 Look for and make use of structure.
CCSS.Math.Content.6.EE.A.4
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
CCSS.Math.Content.6.EE.B.6
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
Answers to classwork: