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Inequality Symbols
Graphing Inequalities
Solving Inequalities
Solving Absolute Value Problems
Absolute Value Word Problems and Interval Notation
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

Re-write it in two equations- one set equal to the positive and one set equal to the negative.

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

Solve

5x-6-3x≤2(x-2)

All real numbers

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.


|x-68|<=2

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

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

Rewrite the absolute value inequality as either a compound AND inequality or a compound OR inequality.

300

Write using interval notation.

x is less than or equal to -3

(- infinity symbol, -3]

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

Rewrite |2x +4| ≤ 10 as a compound inequality.

-10 ≤ 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. 


|x-10|<=2

.

500

This mathematical statement reads " a is less than or equal to b and b is less than or equal to c"

What is a ≤ b ≤ c?

500

Graph the following.

[12,20)

closed circle around 12

open circle around 20

shade in-between the two circles

500

Solve 

-9 ≤ 4x +1 < 10

-5/2 ≤ x < 9/4

500

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

What is |x+2| > 2?

500

Write all problems below using interval notation.

- negative nine is less than or equal to x is less than 10

- x is less than or equal to -4 OR x is greater than 8


[-9,10)

(negative infinity, -4] OR (8, infinity)