Inequality Symbols
Graphing Inequalities
Solving Inequalities
Solving Absolute Value Problems
Tolerance/Variance
100
This mathematical statement reads "a is less than b"
What is a < b
100
These two symbols indicate that you should shade to the left.
What is < and ≤?
100
Solving inequalities is very similar to solving this type of a problem.
What is an equation?
100

You do this in order to remove the absolute value symbols in an absolute value equation

What is to rewrite it in two equations- one positive and one negative or disjunction?

100

A machine at a lumber mill cuts boards that are 3.25 meters long.  It is acceptable for the length to differ from this value by 0.02 meters.  Write and solve an absolute value inequality to find the range of acceptable lengths.

What is

|x-3.25|<=0.02

 and the acceptable lengths of the boards are 3.23 meters to 3.27 meters.

200
This mathematical statement reads " a is greater than or equal to b"
What is a ≥ b?
200
These two symbols indicate that you should use a closed circle when graphing inequalities.
What is ≤ and ≥?
200
When you are getting the variable by itself you are also doing this.
What is isolating the variable?
200
These are the two equations needed to solve |2x +7| = 10
What is 2x +7 = 10 and 2x + 7 = -10?
200

The thermostat for a house is set to 68 degrees F. but the actual temperature may vary by as much as 2 degrees F.  Write and absolute value inequality, and find the range of possible temperatures.

What is

|x-68|<=2

and temperatures can range from 66 degrees F to 70 degrees F?

300
This mathematical statement reads "a is not equal to b"
What is a ≠ b?
300
In this type of compound inequality, you should shade between the two values.
What is an "AND" compound inequality?
300

Solve. 

2x+3 > 5 or 2x+3 < 0 

What is x>1 or x<-1.5?

300
You do this in order to remove the absolute value symbols in an absolute value inequality
What is create two inequalities - one positive and one negative with a flipped inequality symbol?
300

You are playing a History Quiz game where you must give the year of historical events.  In order to score any points at all for a questions about the year in which a man first stepped on the moon, your answer must be no more than 3 years away from the correct answer, 1969.  What is the range of answers that will allow you to score points?

What is

1966<=y<=1972

?

400
This mathematical statement reads "a is at most b".
What is a ≤ b?
400
In this type of compound inequality you should shade outside the two values.
What is an "OR" compound inequality?
400

Another way to write the inequalities -6 < 2x+4 and 2x+4 ≤ 10 as a compound inequality.

What is -6 < 2x+4 ≤ 10?

400

These are the two inequalities needed to solve |2x +4| ≤ 10.

What is 2x+4 ≤ 10 and 2x+4 ≥ -10?

400

The maximum allowable weight of a fountain pen manufactured at the pen factory is 12 grams and the minimum acceptable weight is 8 grams.  Pens not within this range are disposed of.  Write the absolute value inequality that represents the range of acceptable weights. 

What is  

|x-10|<=2

.

500
This mathematical statement reads " a is greater then or equal to b and b is greater then or equal to c"
What is a ≥ b ≥ c?
500

In this type of inequality, there is a pattern in regards to shading between or outside the values.

What is an absolute value inequality?

500
These are the two inequalities that -9 ≤ 4x +1 < 10 is separated into so that you can solve the compound inequality.
What is -9 ≤ 4x +1 and 4x+1 < 10?
500

The inequalities x + 2 > 2 or x + 2 < -2 come from this absolute value inequality

What is |x+2| > 2?

500

The speed limit on a road is 30 miles per hour.  Drivers on this road typically vary their speed around the limit by as much as 5 miles per hour.  Write and solve an absolute value inequality that represents the range of speeds on the roads?

What is

|x-30|<=5

 and the speeds range from 25mph to 35 mph, inclusive .


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