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VOCABULARY
An equation is formed when an equal sign (=) is placed between two expressions creating a left and a right side of the equation
An equation that contains one or more variables is called an open sentence
When a variable in a single-variable equation is replaced by a number the resulting statement can be true or false
If the statement is true, the number is a solution of an equation
Substituting a number for a variable in an equation to see whether the resulting statement is true or false is called checking a possible solution
INEQUALITIES
Another type of open sentence is called an inequality.
An inequality is formed when and inequality sign is placed between two expressions
A solution to an inequality are numbers that produce a true statement when substituted for the variable in the inequality
INEQUALITY SYMBOLS
Listed below are the 4 inequality symbols and their meaning
< Less than≤ Less than or equal to> Greater than≥ Greater than or equal to
Note: We will be working with inequalities throughout this course…and you are expected to know the difference between equalities and inequalities
GRAPHS OF LINEAR INEQUALITIES
Graph (1 variable) The set of points on a number line that
represents all solutions of the inequality
WRITING LINEAR INEQUALITIES
Bob hopes that his next math test grade will be higher than his current average. His first three test scores were 77, 83, and 86.
Why would an inequality be best in this case?
How can we come up with this inequality?
Graph!
SOLVING ONE-STEP LINEAR INEQUALITIES
Equivalent Inequalities Two or more inequalities with exactly the same
solution
Manipulating Inequalities All of the same rules apply to inequalities as
equations*
When multiplying or dividing by a negative number, we have to switch the inequality! Less than becomes greater than, etc.
SOLVING MULTI-STEP LINEAR INEQUALITIES—3.2
ALGEBRA CHAPTER 3 Solving and Graphing Linear
Inequalities
MULTI STEP INEQUALITIES
Treat inequalities just like you would normal, everyday equations*
*change the sign when multiplying or dividing by a negative!!
EXAMPLE
You plan to publish an online newsletter that reports the results of snow cross competitions. You do not want your monthly costs to exceed $2370. Your fixed monthly costs are $1200. You must also pay $130 per month to each article writer. How many writers can you afford to hire in a month?
o-4 -3-5o-4 -3-5●-4 -3-5
-4 -3-5●
1.
2.
3.
4.
Answer NowAnswer Now
1) WHICH GRAPH REPRESENTS THE CORRECT
ANSWER TO > 1k
4
2) WHEN SOLVING > -10WILL THE INEQUALITY SWITCH?
1. Yes!2. No!3. I still don’t
know!
x
3
Answer NowAnswer Now
3) WHEN SOLVINGWILL THE INEQUALITY SWITCH?
1. Yes!2. No!3. I still don’t
know!
a4
6
Answer NowAnswer Now
COMPOUND INEQUALITY
What does compound mean? Compound fracture?
So…what’s a compound inequality? An inequality consisting of two inequalities
connected by an and or an or
GRAPHING COMPOUND INEQUALITIES
Graph the following: All real numbers that are greater than or equal to
-2 and less than 3
SOLVING COMPOUND INEQUALITIES
Again….treat these like equations!
Whenever we do something to one side…
…We do it to every side!
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