Section 1-5 Solving Inequalities
In this lesson you will solve and graph inequalities; and write and solve
compound inequalities.
An Inequality is a relation between two expressions that are not equal. Using
signs like :
≠
Less than <
Not equal
Greater than >
Less than or equal to ≤
Greater than or equal to ≥
The solution of an inequality is the numbers that make it true.
The solution can be a range of numbers and
When solving inequalities you use the same method for solving
equations. However, when you multiply or divide by a
negative number the inequality sign flips.
Example: Solving and graphing
an inequality
Ex)
Graph the solution on a number line.
 3(2 x  5)  1  4
 6 x  15  1  4
 6 x  16  4
 16  16
 6 x  12
 6
 6
x2
0
2
Closed circle when
≥ or ≤
Solving and graphing multi-step inequalities
video. (1 ex, 1 practice)
Compound inequalities: two inequalities joined together
with the word “and” or “or”
AND inequality
5  2 x  1 and 2 x  1  13
5  2 x  1  13
1 1 1
4  2 x  12
2 2 2
2 x6
x  2 and x  6
Writing and solving compound
inequality “AND” video real world
fitness word problem
x≤6
x>2
0 2
AND means that a solution
makes BOTH inequalities
true. Where the lines
overlap
6
OR inequality
7  k  6 OR 8  k  3
7k 6
-7 -7
k  1
-5
OPEN circle
when
<,>
OR
8 k  3
OR
8 8
k  5
-1 0
Writing and solving a
compound inequality
containing OR video. 2 ex) 1
word problem
ALWAYS, NEVER, SOMETIMES?
If the statement is always
true, ALL real numbers are
solutions
If the statement is false, then
the inequality has no solution
Inequalities with no solution or all
real numbers as solutions video. 1
ex) 1 practice, party budget
x  4 or x  5
-5
0
4
x  4 and x  5
-4
0
5
Practice

Standard Pg. 38 #11-43 odd, 44-61

Honors Pg 38. #11-43 odd, 44-66

Standardized test prep: 67-70
ANSWERS in back of book
Lesson quiz 1-5

1. What inequality represents the sentence, “The product of:
and a number is less than 20”?

2. What is the solution of -5(2x - 1) + 3 ≤ -2?
Graph the solution.

3. Do you UNDERSTAND? Eastside Gym charges a $60 initial fee
and $28.50 per month. Valley Gym charges $36 per
month, and no initial fee. After how many months of use
would Eastside cost less than Valley?

4. Is the inequality sometimes, always, or never true?
3(4x + 2) + x ≤ 1 + 13x

5. What is the solution of 2 ≤ 3x + 8 and 20 > 4x?
Graph the solution.
Quiz answers
6