Solving Two-Step Inequalities
Warm Up
Solve each
inequality.
Graph and
check the
solution.
Find 3 possible solutions to the given
inequalities.
x + 7 < 12
-4 – b > 20
8y ≥ -16
𝑎
−6
≤1
• Solving two-step inequalities is similar to
solving two step equations. You must isolate
the variable by performing the same
operation on both sides of the inequality.
• The direction of the inequality symbol changes
when both sides of the inequality are
multiplied or divided by a negative number.
• It is important to distinguish between the
phrases “greater than” and “greater than or
equal to” and the phrases “less than” and
“less than or equal to.”
During the year Ms. Torres paid
$1,200 for car repairs and bought 4
new tires. The total amount she
spent on her car for repairs and
tires was less than $1,820.
How much did each new tire cost?
Justify your answer.
Solve
5f + 11 ≤ -4
Ed wants to bicycle at least 75
miles this week. The inequality
11 + 4b ≥ 75 can be used to find b,
the average number of miles he
should bike on his remaining 4 bike
rides this week. Solve the
inequality, and graph the solution
set on a number line.
Dianna is buying lunch for herself and
two friends. She has a coupon for $15
off the total bill and wants to spend
less than $49 after using the coupon.
The equation 3m - 15 < 49 can be used
to find m, the average price of each
friend’s lunch. Determine which, if
any, of the following values make the
equation true: m = 21; m = 22; m = 23.
𝑦
The inequality −𝑦 𝑥 + 𝑦 ≥ −𝑦
has the solution x ≤ 10 for a certain
value of y. Use substitution and
guess-and-check to find the correct
value for y. Explain how
you know your answer is correct.
Exit Ticket
1. Solve
2.
3.
4.
5.
𝑥
3
− 10 ≤ 11
Solve 52 > -12 + 8d
Solve -16p + 111 ≥ -65.
Charlene is a writer who is going on a trip. She has
brought several copies of her latest book in her
suitcase. The suitcase itself weighs 5 pounds, and each
book weighs 3 pounds. If her full suitcase can weigh
no more than 50 pounds, how many books can she
bring?
Carl is having a party. He has bought 24 brownies and
is making 6 more batches of brownies. The inequality
24 + 6b ≥ 138 can be used to determine how many
brownies, b, must be in each batch so that all 138
guests get at least 1 brownie. Determine which of the
given values, if any, make the inequality true: b = 10; b
= 15; b = 20.