5.3 Solving Multistep Inequalities
Algebra 1
Inequality:
The relationship
between two
expressions that are
NOT necessarily
equal.
<
Name:
_________________________
>
≤
Example #1: Solve a Multi-Step Inequality
1A. Adriana has a budget of $115 for faxes.
The fax service she uses charges $25 to activate
an account and $0.08 per page to send faxes. How
many pages can Adriana fax and stay within her
budget? Use the inequality 25 + 0.08p ≤ 115.
≥
1B. Rob has a budget of $425 for senior pictures.
The cost for a basic package and sitting fee is $200. He
wants to buy extra wallet-size pictures for his friends
that cost $4.50 each. How many wallet-size pictures
can he order and stay within his budget? Use the
inequality 200 + 4.5p ≤ 425.
Example #2: Inequalities Involving Negatives
2A. Solve: 13 − 11𝑑 ≥ 79
2B. Solve: −8𝑦 + 3 > −5
Remember:
When multiplying or
dividing by a
negative number, we
MUST flip the
inequality!
Example #3: Writing & Solving Inequalities
5.3 Solving Multistep Inequalities
Algebra 1
Name:
_________________________
Example #4: Solving with Distributive Property
4A. Solve: 6𝑐 + 3(2 − 𝑐) ≥ −2𝑐 + 1
4B. Solve:
3𝑝 − 2(𝑝 − 4) < 𝑝 − (2 − 3𝑝)
Example #5 and #6: Empty Sets and All Real Numbers
5. Solve: −7(𝑠 + 4) + 11𝑠 ≥ 8𝑠 − 2(2𝑠 + 1)
6. Solve: 2(4𝑟 + 3) ≤ 22 + 8(𝑟 − 2)
You Try!
Solve: 8𝑎 + 5 ≤ 6𝑎 + 3(𝑎 + 4) − (𝑎 + 7)
Remember:
When you reach a false
3A. Fourstatement…your
times a number plus twelve is less than the
number minus
three. is the empty
solution
set!
You Try!
Solve: 4𝑟 − 2(3 + 𝑟) < 7𝑟 − (8 + 4𝑟)
Remember:
When you get the same
expression on both sides, this
3B. 6 times a number is greater than 4 times the
means that any value you plug
number minus 2.
in with satisfy the
inequality...ALL REAL
SOLUTIONS!
5.3 Solving Multistep Inequalities
Algebra 1
Name:
_________________________
Helpful
Hints!