Lesson 1-8: An Introduction to Equations
1-8.1 – Classifying Equations
Vocabulary:
Equation – A mathematical sentence that uses an equal sign
Open Sentence – An equation that contains one or more variables and may be true or false depending on
the values of those variables.
We need to be able to determine if an equation is true, false or open.
Examples:
OpenTrueFalse
1-8.2 – Identifying a solution to an equation.
Vocabulary:
Solution to an equation – The value of the variable(s) that makes the equation true
To determine if a variable is a solution to an equation or not, we must substitute the value into the equation and solve the equation.
Examples:
Is x = 6 a solution of the equation?No, because it gives you which is not true.
Is a solution of the equation Yes, because it gives you which is true.
Is x = 27 a solution of the equation ?Yes, because it gives you 14 = 14 which is true.
1-8.3 – Writing an equation.
To write an equation we are going to use the same bank of words for the operations we used in lesson 1-1. We just have to recognize words that will tell us where to place an equal sign.
So words that mean equal would be? Equal, Is, Same as, Solution, Answer etc.
Example: The sum of 4x and 3 is 8:
John has $48 less than Peter: P – 48 = J
1-8.4 – Using Mental Math or a Table to Find a Solution.
Sometimes you can look at an equation and see a solution to an equation. For example, x + 8 = 12 is an easy equation to look at and tell that x needs to be 4 to make this true.
Other Examples:
If you cannot find the solution mentally, you can use a table to narrow the answer down.
Examples:
Find the value of Find the value of
n / 5n + 8 / Value5 / 5(5)+8 / 33
6 / 5(6)+8 / 38
7 / 5(7)+8 / 43
8 / 5(8)+8 / 48
p / / Value
-5 / / 40
-8 / / 49
-10 / / 55
-11 / / 58
So 8 is the value of n that make the equation true So -11 is the value that makes the equation true
We can also use a table to estimate a solution.
Example:
x / / Value2 / / 13
3 / / 22
4 / / 31
So the solution would be between 3 and 4 closer to 4