Algebra Honors ( Periods 6 & 7)

Inequalities in One Variable
Order of Real Numbers 10-1

This sections should be review... you have been working with less than and greater than symbols since 6th grade. A number line shows order relationships among all real numbers. The value of a variable may be unknown but you may know that is either greater than or equal to another number.
For example,
x ≥ 5 is read "x is greater than or equal to 5."
x ≥ 5 is another way of writing " x >5 or x = 5"

Translating statements into symbols is a critical concept. Practice these as review
-3 is greater than -5.    -3 > -5
and
x is less than or equal to 8  x    ≤   8

To show that x is between -4 and 2 you write
-4 < x < 2
which is read 
"-4 is less than x and x is less than 2."
or you could read it as
" x is greater than -4 AND less than 2."

The same comparisons are stated in the sentence  2 > x  > -4

When all the numbers are know you can classify the statement as true or false.
Thus,
-4 < 1 < 2   is true
but
-4 < 8 < 2 is false

An inequality is formed by placing an inequality symbol (  > ,  < ,     ≤ , or    ≥) between numerical pr variable expressions-- called the SIDES of the inequality
You solve an inequality by finding the values from the domain of the variable which make the inequality a true statement.   Such values are called the solutions of the inequality. All the solutions make up the solution set of the inequality.