Warm
Up
Write as an algebraic expression.
1. the product of 12 and the sum of a number and 5
Solve.
2. −2 3𝑦 − 6 + 4 5𝑦 − 8 = 92
3.
𝑥+5 =9
4. 3 2𝑥 − 3 − 5 = 4
1.5 Solving Inequalities
This symbol: < is read as…
> is read as…
≤ is read as…
≥ is read as…
Solving
Our goal is to have the variable
on its own on the left of the
inequality sign. Like this…
𝑥 < 13
𝑦 ≥ −2
How to Solve
Solving inequalities is just like
solving equations.
One extra detail to pay attention to
is the direction of the inequality.
small
BIG
Safe Things to Do
These are things you can do without
affecting the direction of the
inequality.
o Add or subtract a number from both
sides
o Multiply or divide both sides by a
positive number
o Simplify a side
Changing Direction
BUT these things will change
the direction of the inequality.
o Multiply or divide both sides by a
negative number
o Swapping left and right hand sides.
Changing Direction
Changing direction means…
< would become >
would
become
>
<
≤ would become ≥
≥ would become ≤
Solving Inequalities
1. Get the variable on its own on
the left of the inequality sign.
2. Graph the inequality on a
number line.
o
●
→
←
Open circle: < and >
Closed circle: ≤ and ≥
Arrow pointing right: > and ≥
Arrow pointing left: < and ≤
Examples
Solve each inequality. Then graph the
solution set on a number line.
1. 𝑦 − 6 < 3
2. 4𝑥 − 4 > 6𝑥 + 2
Examples
Solve each inequality. Then graph the
solution set on a number line.
1. 3𝑎 + 7 ≤ 16
2. −3𝑛 > 7𝑛 + 20
3. 4𝑏 − 9 ≤ 7
You Try!
Solve each inequality. Then graph the
solution set on a number line.
1. 5𝑤 + 3 > 4𝑤 + 9
2. −5𝑦 − 3 < −4𝑦 + 2
You Try!
Solve each inequality. Then graph the
solution set on a number line.
1. 16 − 3𝑞 < 4
2. 3𝑥 ≥ −9
Word Problems
1. An adult panda bear (P) will
eat at least 20 pounds of
bamboo every day. Write an
inequality that expresses this
situation.
Word Problem
2. On a Ferris wheel at a carnival, only two
people per car are allowed. The two people
together cannot weigh more than 300
pounds. Ron and his father want to go on the
ride together. Ron’s father weighs 175
pounds.
a) Write an inequality that expresses this situation.
b) Draw a visual representation on a number line, and
c) Solve the inequality to find the maximum weight
Ron (𝑥) can be for the two to be allowed on the
ride?
Word Problem
3. Rosa’s cell phone plan costs her $50 per
month plus $0.25 for each minute she goes
beyond her free minutes. How many
minutes (𝑚) can she go beyond her free
minutes and still pay less than a total of $70?
a) Write an inequality that expresses this
situation.
b) Draw a visual representation on a number
line, and
c) Solve the inequality.
Ticket Out The Door
1.
Write an absolute value equation that
corresponds to…
Tara is delivering bags of mulch. Each bag weighs 48
lbs., and the push cart weighs 65 pounds. If her flat-bed
truck is capable of hauling 2000 lbs., how many bags of
mulch (𝒎) can Tara safely take on each trip?
2. Draw a visual representation on a
number line, and
3.
Solve the inequality.
Homework
Lesson 1.5
Pg. 37 #’s 10-21