Name __________________________________________ Date __________
7th Grade Honors Mathematics
Mrs. Mazzarella
Class Notes: Solving Multi-Step Inequalities
Aim: How do we solve multi-step inequalities?
Do Now:
The inequality below compares the value of a $20 bill to the value of a $10 bill.
20 > 10
1.) Add $5 to the value of each bill and
write an inequality to compare their
new values.
20 > 10
+5 +5
__________________
2.) Subtract $5 from the value of each
bill and write an inequality to
compare their new values.
20 > 10
–5 –5
__________________
3.) Multiply the value of each bill by 2
and write an inequality to compare
the value of two $20 bills to two $10
bills.
20 > 10
×2 ×2
__________________
4.) Divide the value of each bill by 2 and
write an inequality to compare half
the value of a $20 bill to half the
value of a $10 bill.
20 > 10
2
2
__________________
5.) Multiply the value of each bill by -1
and write an inequality to compare
the status of being $20 in debt to
Whole
Group
being $10
in debt.Questions
__________________
20 > 10
× -1 × -1
Whole Group Instruction:
-GUIDED INSTRUCTION-
1.) She bought 8 notebooks, used a coupon to save $4, and spent more than $12 total.
a.) Solve the inequality to find
the possible cost of a notebook.
b.) Choose a number from the
solution set to check.
8n – 4 > 12
c.) Graph the solution set.
2.) a.) Solve the inequality to find
the solution set.
b.) Choose a number from the
solution set to check.
-2n + 10 ≤ 20
c.)
Graph the solution set.
Small Class Instruction/Independent Practice:
Solve and Check
1.) 11(x – 4) > 55
CHECK
2.) -3n + 9 ≥ 3
CHECK
Solve and Graph
3.)
1
(n + 10) ≥ 15
2
4.) -5x – 10 < 30
5.)
x
 5  8
2
6.) 8 
x
< 7
3
Summary Questions
1.) How is solving an inequality similar to solving an equation?
2.) How is the solution set of an inequality different than the solution of an equation?
3.) Which inequality below requires reversing the comparison symbol when
solving, and why?
A
-5x > 30
B
2x ≤ -10
Additional Examples:
1.) Luke is making some money by shoveling snow. He makes $10 per house and he
already had $50 saved before he started working.
Solve the inequality below to see how many houses, h, Luke may have
shoveled if he had at least $200 at end of the day.
10h + 50 ≥ 200
2.) Gloria is getting ready to fly on an airplane. She went to the airport’s gift shop and
bought a bottle of Gatorade for $2 and 3 magazines that were each the same
price.
Solve the inequality below to find the possible price of each magazine, m, if
Gloria spent a maximum of $14.
3m + 2 ≤ 14
Name: ____________________
7th Grade Honors Mathematics
Date __________
Mrs. Mazzarella
HOMEWORK: Solving Multi-Step Inequalities
Aim: How do we solve multi-step inequalities?
Directions: Solve, check, and graph the inequalities below.
1.) 3(n – 2) ≤ 30
CHECK
2.) 34 + 2g > 62
3.) -20 > -2x + 4
CHECK
4.)
x
9 <5
2
CHECK
CHECK
Name __________________________________________ Date __________
7th Grade Honors Mathematics
Mrs. Mazzarella
Class Notes: Solving MORE Multi-Step Inequalities
Aim: How do we solve multi-step inequalities?
Whole Group Instruction:
-GUIDED INSTRUCTION-
Solve, Check and Graph Please come up with a solution set before you
graph the inequality.
1.) 4 (x - 1 ) < 16
CHECK
2.) -5y + 3 > 13
CHECK
Small Class Instruction/Independent Practice:
Solve and Graph Please come up with a solution set before you graph the
inequality.
1.) 8m - 6 > 34
2.) 3 (x + 4) < -9
Whole Group Instruction:
-GUIDED INSTRUCTION-
Word Problems:
1.) Luke is making some money by shoveling snow. He makes $10 per house and he
already had $50 saved before he started working.
Solve the inequality below to see how many houses, h, Luke may have
shoveled if he had at least $200 at end of the day.
IDENTIFY WHAT THE VARIABLE REPRESENTS FIRST!
10h + 50 ≥ 200
Small Class Instruction/Independent Practice:
2.) Gloria is getting ready to fly on an airplane. She went to the airport’s gift shop and
bought a bottle of Gatorade for $2 and 3 magazines that were each the same
price.
Solve the inequality below to find the possible price of each magazine, m, if
Gloria spent a maximum of $14.
IDENTIFY WHAT THE VARIABLE REPRESENTS FIRST!
3m + 2 ≤ 14
3.) Janet went to the food store and bought numerous boxes of pasta for $2 each. Janet
had a coupon for $5 off her purchase. When the cashier gave her, her bill, Janet
still spent at least $13.
Solve the inequality below to find out the minimum number of boxes of pasta,
p that Janet could have purchased.
IDENTIFY WHAT THE VARIABLE REPRESENTS FIRST!
2p – 5 > 13
ADDITIONAL EXAMPLES:
Solve, Check and Graph
3.)
x
 5  8
2
CHECK
4.) 8 
x
< 7
3
CHECK
Summary Questions
1.) How is solving an inequality similar to solving an equation?
2.) How is the solution set of an inequality different than the solution of an equation?
3.) Which inequality below requires reversing the comparison symbol when
solving, and why?
A
-5x > 30
B
2x ≤ -10