Algebra
6.1
Solving One-Step Inequalities
Two Mistakes on This Slideshow

See if you can spot them!
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
x≤4
The graph of an inequality is the set of
points on a number line that are solutions.
The graph is a boundary point and a line
with an arrow pointing left or right.
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
x>2
A hollow point means that the
number is not included in the set
of solutions.
Use a hollow point to graph < and >
inequalities.
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
x ≥ -3
A solid point means that the number is
included in the set of solutions.
Use a solid point to graph ≤ and ≥
inequalities.
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
x < -1
The arrow points left for < and ≤ .
The arrow points right for > and ≥ .
The direction of the arrow tip is the same
as the direction of the inequality symbol
when the variable is on the left side.
Solve inequalities just as you would
linear equations in one variable. Isolate
the variable. Then graph the solution.
x - 5 > -4
+ 5 +5
x > 1
15a ≤ -60
15
15
a ≤ -4
-1
0
1
2
3
4
-7
-6
-5
-4
-3
-2
The only difference between solving an
inequality and an equation is what
happens when both sides are multiplied
or divided by a negative value.
> 5 (2) Multiply by positive
20 > 10 Inequality stays true
(-2) 20 > 10 (-2) Multiply by negative
-40 > -20 Inequality not true
(2) 10
-40
<
-20
Reverse direction of
inequality symbol
When solving an inequality,
REVERSE THE DIRECTION OF THE
INEQUALITY SYMBOL if you multiply or
divide by a negative value.
 4
 
 3
-¾a
a
≥
≤
6
-8
 4
 
 3
Multiply by -4/3
Reverse direction of
inequality symbol
Solve the following inequalities and
graph each solution.
¼x > -8
x > -32
-34
a

 5
10
-33
-32
-31
-30
-29
51
52
a ≤ 50
47
48
49
50
Solve the following inequalities and
graph each solution. Write the variable
on the left in your solution.
42 > x
x < 42
x
6  
7
39
40
41
42
43
44
-1
0
-3 < x
x > -3
2 > -1 - x
-5
-4
-3
-2
Homework
Pg. 337 #31 – 61 odd, 71-87