Name
The calendar and all assignments are subject to change. Students will be notified of any changes
during class, so it is their responsibility to pay attention and make any necessary changes. All
assignments are due the following class period unless indicated otherwise.
April 11
12
Intro to Inequalities
SAT
13
Juniors test in the
morning
Solving
Inequalities- One
Step and graphing
the solution
Juniors Only
4-6 hours only
18
Solving
InequalitiesDistributive
Property
19
14
20
MAP Testing
Solving
InequalitiesVariable on both
sides
15
Solving two step
inequalities
21
22
Quiz #7B
Review Solving
Inequalities
Solving Inequalities
Sometimes we need to solve Inequalities like these:
Our aim is to have
Symbol
Words
Example
>
greater than
x+3>2
<
less than
7x < 28
≥
greater than or equal to
5≥x-1
≤
less than or equal to
2y + 1 ≤ 7
x (or whatever the variable is) on its own on the left of the inequality
sign:
We call that "solved".
Something like:
or:
x<5
y ≥ 11
1
Pre – Algebra Solving Inequalities

What is an inequality? How can we represent all the solutions to an inequality?
Graph the following:
1.
X>-3
2.
X<6
3.
4>x
Solve.
1.
a) x – 4 = 8
b)
x–4>8
2
2. a) x + 5 = 9
b)
3. a) 3 = x - 7
b) 3 > x - 7
4>2
-6 < 8
x+5 <9
-2 > -10
6 > -4
Multiply by 2
Multiply by - 2
Divide by 2
Divide by -2
Make a conjecture regarding what you see in the chart above.

How is solving an inequality like solving an equation?

How is solving an inequality different than solving an equation?
3
Solve each inequality. Graph the solution.
x
 2
2
(a)
-6 -5 -4 -3 -2 -1 0 1
x
 2 x  6
(c)
3x  33
(b)
0 2
(d)
x
4 6 8 10 12 14
x
5
4

-2 -1 0 1 2 3 4 5
x
-30 -20 -10 0 10 20 30 40
x
Solving Two Step Inequalities
1.
2x – 3 = 7
2.
3.
½x – 3 = -11
4.
2x – 3 > 7
½x – 3 < -11
4
5.
7.
23 – 5x = 15
- x + 5 = -2
6.
23 – 5x < 15
8.
- x + 5 = -2
 So if you know how to solve a two-step equation, then
 There are two differences:
o To show all the answers,
o When you multiply or divide both sides of the equation by a
negative, you
5
What about Distributive Property with Inequalities??
Solve the inequality. Graph the solution.
1. 2b  4   6
2.
 8 p  3  16
5
15

d  6
3.
3
4.
3.4  0.4a  12
5. Write and solve an inequality that represents the
values of x for which the area of the rectangle
will be at least 35 square feet.
6. You are renting a moving truck for a day. There is a daily fee of $20 and a
charge of $0.75 per mile. Your budget allows a maximum total cost of $65.
Write and solve an inequality that represents the number of miles you can
drive the truck.
6
Practice Solving Multi-Step Linear Inequalities
Solve each inequality. Then graph the solution.
(a) 5x  3  12
(b)  3x  1  22
-2 -1 0 1 2 3 4 5
x
(c)  x  1  3x  21
-7 -5 -3 -1 1 3 5 7
-7 -5 -3 -1 1 3 5 7
x
(d) 2 x  4  4 x  1
x
-2 -1 0 1 2 3 4 5
x
7
Solving More Inequalities
Solve the following inequalities.
1. 3x  7 x  2  10  12
2.
14w  8w  5.4  7.3  10
3. 12x  5x  4  60  8
4.
4v  6v  3.2  6.8  9.2
5. 4 x  1   6
x5
 2
7.
6
6.
1
 x  28  11
2
8.
2x  1
1
4
8