Download 3.2 & 3.3 One-Step Inequalities

U1-S3-L2 One-Step Inequalities
Essential Question:
How do you solve and graph one-step
inequalities?
RULES FOR INEQUALITIES
1) GOAL: Isolate the variable on
ISOLATE
one side of the inequality.
2) Always perform the same
operation to both sides of an
inequality to keep it balanced. BALANCE
3) To undo an operation,
INVERSE
perform its opposite operation
OPERATION
to both sides of the inequality.
VOCABULARY & Key Concepts
• Equivalent Inequalities:
inequalities with the same
solution set.
• When multiplying or dividing by a
negative number, you must
reverse the inequality symbol to
keep it true.
Inequalities
Inequalities
Inequalities
Set-Builder Notation
One-Step Addition & Subtraction
• Solve just like equations: use the inverse operation!
Examples:
1) x + 9 < 15
2) d – 3 > -6
3) 0.7 > n – 0.4
The solutions of x + 9 < 15 are
given by x < 6
Practice
One-Step Multiplication &
Division
• Solve just like equations: use the inverse operation!
• Examples:
1) 3x > -27
2) 2 r  6
3
Practice
Negative Numbers
One-Step Multiplication &
Division
• If the number with the variable is negative, you must reverse the
inequality symbol when you do the inverse operation!
• Examples:
1) -8x > 72
2)
x
3
5
Practice
• Solve each inequality and graph the solution. Check your answer.
2a. -12x > 84
2b.
x
8 
3
2c. 4.25 > -0.25h
Extension
1) Sami has a gift card. She has already
used $14 of the of the total value, which
was $30. Write, solve, and graph an
inequality to show how much more she
can spend.
Answer
3
Solve
g + 14 ≤ 30
– 14 – 14
g + 0 ≤ 16
Since 14 is added to g, subtract
14 from both sides to undo the
addition.
g ≤ 16
It is not reasonable for Sami to spend a
negative amount of money, so graph numbers
less than or equal to 16 and greater than 0.
0
2
4
6
8 10 12 14 16 18 10
Extension
2) A certain restaurant has room for 120
customers. On one night, there are 72
customers dining. Write and solve an
inequality to show how many more people
can eat at the restaurant.
x + 72 ≤ 120; x ≤ 48, where x is a natural
number
Extension
3) A soccer coach plans to order more shirts
for her team. Each shirt costs $9.85. She
has $77 left in her uniform budget. What
are the possible numbers of shirts she can
buy?
0, 1, 2, 3, 4, 5, 6, or 7 shirts
Check for Understanding
1) How is solving inequalities similar to
solving equations?
2) How is the solution of an inequality
different from the solution of an
equation?
Summary
• Answer the essential questions in detailed,
complete sentences.
• How do you solve and graph one-step
inequalities?
• Write 3-5 study questions in the left
column to correspond with the notes.