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Today’s Lesson
Solving One-Step
Linear Inequalities
Unit 3-Lesson 8
Warm-up Activity
Let’s warm up today
by writing expressions
and equations.
Work with a partner to solve the
following problems.
The sum of a number and –2.3 is 7.82.
Let x = a number
x + (–2.3) = 7.82
+2.3 +2.3
x = 10.12
to “undo” a negative you
must use a positive
What you do to one side
of the equation, be sure
and do to the other.
The difference of a number
and –2.3 is 7.82.
Let x = a number
x – (–2.3) = 7.82
x + 2.3 = 7.82
–2.3 –2.3
x = 5.52
minus a negative is a
positive
to “undo” addition you
must subtract
What you do to one side
of the equation, be sure
and do to the other.
The product of –2.3 and a
number is 7.82.
Let x = a number
–2.3x = 7.82
–2.3
– 2.3
x = –3.4
to “undo” multiplication
you must divide
What you do to one side
of the equation, be sure
and do to the other.
The quotient of a number
and –2.3 is 7.82.
Let x = a number
x
(– 2.3) –2.3 = 7.82 (– 2.3) to “undo” division
you must multiply

x = –17.986
What you do to one side
of the equation, be sure
and do to the other.
The product of –2.3 and the sum of a
number and 2 is 7.82.
Let x = a number
–2.3(x + 2) = 7.82
–2.3x – 4.6 = 7.82
+ 4.6 + 4.6
–2.3x = 12.42
–2.3 – 2.3
x = –5.4
distribute the –2.3
to “undo” subtraction
you must add
What you do to one side
of the equation, be sure
and do to the other.
Whole-Class Skills Lesson
Today we will be solving
one-step linear equations.
Each inequality has two choices:
true or false.
Determine which choice is true
for each inequality.
Then, read the inequality.
2+x<8
if x = 5 or if x = 10
Determine which choice is true for the inequality.
2+5<8
True for x = 5
2+x<8
–2
–2
x<6
or
2 + 10 < 8
What you do to one side of
the inequality, be sure and
do to the other.
to “undo” addition you
must subtract
2+x<8
The sum of 2 and a number is
less than 8.
True for x = 5.
True for x < 6.
x – 1.2 > –12
if x = –15 or if x = 10
Determine which choice is true for the inequality.
–15 – 1.2 > –12
or
10 – 1.2 > –12
True for x = 10
x – 1.2 > –12
+ 1.2
+ 1.2
x > –10.8
What you do to one side of
the inequality, be sure and
do to the other.
to “undo” subtraction you
must add
x – 1.2 > –12
The difference of a number and 1.2
is greater than –12.
True for x = 10.
True for x > –10.8.
–x < 8
if x = –10 or if x = 10
Determine which choice is true for the inequality.
–(–10) < 8
10 < 8
–x < 8
–1
–1
x > –8
or
–10 < 8
True for x = 10
When you multiply or divide both
sides of an inequality by a negative
number, the direction of the
inequality must be changed.
–x < 8
The opposite of a number is
less than 8.
True for x = 10.
True for x > –8.
2x ≥ –8
if x = –10 or if x = 10
Determine which choice is true for the inequality.
2(–10) ≥ –8
–20 ≥ –8
2x ≥ –8
2
2
x ≥ –4
or
2(10) ≥ –8
20 ≥ –8
True for x = 10
2x ≥ –8
Two times a number is greater
than –8.
True for x = 10.
True for x ≥ –4.
–2x ≤ 8
if x = –10 or if x = 10
Determine which choice is true for the inequality.
–2(–10) ≤ 8
20 ≤ 8
–2x ≤ 8
–2
–2
x ≥ –4
or
–2(10) ≤ 8
–20 ≤ 8
True for x = 10
When you multiply or divide both
sides of an inequality by a negative
number, the direction of the
inequality must be changed.
–2x ≤ 8
Negative two times a number is
less than or equal to 8.
True for x = 10.
True for x ≥ –4.
–2x ≥ –8
if x = –10 or if x = 10
Determine which choice is true for the inequality.
–2(–10) ≥ –8
or
–2(10) ≥ –8
20 ≥ –8
True for x = –10
When you multiply or divide both
sides of an inequality by a negative
number, the direction of the
inequality must be changed.
–20 ≥ –8
–2x ≥ –8
–2
–2
x≤4
–2x ≥ –8
Negative two times a number is
greater than or equal to –8.
True for x = –10.
True for x ≤ 4.
x
> –1.2
3

3 1
  x > –1.2
1 3
3
 
1 
x > –3.6


1
3
Dividing by is the same as
3
multiplying by 1 (the reciprocal).
x
> –1.2
3
A number divided by 3 is
greater
than
–1.2

x 
–  <
5 
5  1 
–  – x <
1  
5 
–0.6
–0.6
5 
– 
1 
x > –3
1
5
Dividing by is
the same as
5
multiplying by 1

(the reciprocal).


When you multiply or divide both sides of an
inequality by a negative number, the
direction of the inequality must be changed.
x 
–  <
5 
–0.6
The opposite of a number

divided by 5 is less than –
0.6