Chapter 4: Inequalities
Section 4.1—Writing and Graphing Inequalities
What’s the difference between an equation and an inequality?


Equation
Sign between 
the two
expressions is
an = sign

Only one
number is
the solution

Inequality
The sign between the two expressions is an inequality
symbol: <, >, ≤, ≥
More than one number can be the solution to an
inequality—all of the values that make the inequality true
is part of the solution set
The graph of the solution set represents all the values that
make the inequality true—shade the part of the line where
the solutions lie; it’s a ¾ ¾¾® with an open (o) or
Ray

Graph is a
point on the
line at the
solution
•
closed ( ) dot as its endpoint

Read the inequality from the variables:
x ≥ –9  “x is greater than or equal to –9”
½ > y  “y is less than ½”
By doing this, it is easier to graph!
“Less left; Greater right

o “open dot” represents that the value is NOT part of the
solution set (used with < or >)

•
“closed dot” represents that the value IS part of the
solution (used with ≤ or ≥)
Number Line: Be sure it is scaled correctly
Writing Inequalities: Words to Watch
greater than, less than, no more than, no less than, at most,
at least, maximum, minimum
*Always write the inequality with the variable first
e.g. the temperature is at the most 56°F  t ≤ 56


Remember the steps in writing, solving, and graphing equations
Refer to your “Solving Equations” handout
Section 4.2 Solving Inequalities Using Addition or Subtraction
(“Simple” Inequalities—One-Step)
 Like solving equations of the same form—treat them as equations
 Eliminate the constant term—create a zero pair (ZP)
 Remember how to graph the solution set using what we practiced in
Section 4.1—“Opened or closed dot; left or right?”—Always read it from
the variable!
Solving inequalities involving
Subtraction—examples
Solving inequalities involving
Addition—examples
Solving word problems involving inequalities
Section 4.3 Solving Inequalities Using Multiplication or Division
(“Simple” Inequalities—One-Step)
 Like solving equations of the same form—treat them as equations
 Eliminate the coefficient of the variable—you want to get the coefficient
to be “1”
 Remember to graph the solution set using what we practiced in Section
4.1—“Opened or closed dot; left or right?”—Always read it from the
variable!
 The big “BUT” when solving inequalities involving a negative coefficient—
YOU MUST “FLIP” THE DIRECTION OF THE INEQUALITY SYMBOL—if
you don’t, your solution set will be all the values making the inequality
FALSE! (and you don’t want to do that!)
Solving inequalities involving
Division—examples
Solving inequalities involving M
Multiplication—examples
Solving word problems involving inequalities
Section 4.4 Solving Two-Step (and Multi-Step) Inequalities
 Like solving equations of the same form—treat them as equations
 Follow the “Solving Equations” steps from last chapter
 Remember to graph the solution set using what we practiced in Section
4.1—“Opened or closed dot; left or right?”—Always read it from the
variable!
 Remember the “but” when dealing with a negative coefficient—YOU
MUST “FLIP” THE DIRECTION OF THE INEQUALITY SYMBOL
Solving two-step inequalities
Solving multi-step inequalities
Solving inequalities involving division—
e.g. Finding the average of a set of data or missing piece of data