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MATH 7
Linear Inequality in
One Variable

LESSON
OBJECTIVES
?Defines the terms
‘linear inequality in
one variable’.
?Differentiates linear
inequality in one
variable from linear
equation in one
variable.
KNOWLEDGE
?Illustrates a
linear inequality
in one variable.
SKILLS
? Appreciates the
representation of
linear inequalities in
one variable in real
life.
?Cooperates with
other group
members during
group activities.
ATTITUDE

Review
Classify each
of the following
as an algebraic
expression,
equation, or
inequality.

?. ? + ? = ?
?. ??? ? ?? > ?
?. ?? ?? ? ?
?. ?? ≤ ?
?. ? +
?
?
≥ 8 linear inequality in one variable
linear equation in one variable
linear inequality in one variable
algebraic expression
linear inequality in one variable

?. ? + ? = ?
?. ??? ? ?? > ?
?. ?? ?? ? ?
?. ?? ≤ ?
?. ? +
?
?
≥ 8
What is the symbol used in item 1 for it
to be classified as a linear equation?
How did you know that the expression
in item 3 is an algebraic expression?
What is the symbol used in items 2, 4
and 5 for them to be classified as linear
inequalities?
Aside from the symbols used in items
2, 4, and 5, what is the other symbol for
inequality?

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On the other hand, if an expression relates two
expressions or values with a ‘<’ (less than) sign, ‘>’
(greater than) sign, ‘≤’ (less than or equal) sign or ‘≥’
(greater than or equal) sign, then it is called as an
Inequality
Mathematical/ Algebraic expressions help us convert
problem statements into entities and thus, help solve them. If
the expression equates two expressions or values, then it is
called an equation.
For e.g. 3x + 5y = 8. If it is a linear equation in one
variable, an example is 6x-7=0.
6

“
7
Mind the symbols
A linear inequality in
one variable is an inequality
which can be put into the form
?? + ? > ?, where a, b, and c
are real numbers.
Note that the “> "can be
replaced by ≥, <, or ≤.

“
8
Examples:
2? > 4
2? ? 2 < 6? ? 5 ??? ?? ??????? ? 4? + ?2 < ?5.
Then, it would be -4x - 2< -5.
6? + 1 ≥ 3 ? ? 5 ??? ?? ??????? ?? 6? + 1 ≥ ?15
How would each look like if it were
in standard form?

“
9
How would each look like if it were in
standard form?
2? > 4
-4x - 2< -5
6? + 1 ≥ ?15
??????: 2? ? 4 > 0
??????: 4? + 3 > 0
??????: 6? + 16 > 0

“
10
Activity 1: Clap twice if the equation or inequality in one variable
is in standard form and clap once if it’s not.
? ≥ 5
2-5x=6
2(3x-4) >8
3x-15=
2x+2≤ 0

“
STEPS IN TRASFORMING ANY LINEAR INEQUALITY IN ONE
VARIABLE INTO STANDARD FORM
Let us rewrite the following linear
inequalities in the form ax+ b>0.
?. 2? ? 1 < 3? + 5
?. ?
?
3
+ 3 ≥ 4

“
Step 1: First, we need to remove the
fraction/s by multiplying each term by
the LCM (Least Common Multiple )if there
is/ are fraction/s in the given inequality.
?. 2? ? 1 < 3? + 5
Since there is no fraction present in this
inequality, we will move on to step 2.

“
Step 2: Next, apply the necessary properties of
inequality so that only zero is left on the right side
of the inequality.
2? ? 1 < 3? + 5
-3x
-x - 1 < 5
? 5 ? 5
?? ? 6 < 0

“
Step 3: If the leading coefficient, a is negative,
then, multiply Then, since our a term is negative,
we multiply everything by ?1 to make it positive.
(?1)(?? ? 6) < 0(?1)
? + 6 < 0
Where:
a=1, b=6

“
First, we need to remove the fraction/s by
multiplying each term by the LCM.
b. ?
?
3
+ 3 ≥ 4
(3)(?
?
3
+ 3) ≥ (4)(3)
?? + 9 ≥ 12
b. ?
?
3
+ 3 ≥ 4

“
STEPS IN TRASFORMING ANY LINEAR INEAQUALITY IN ONE
?? + 9 ≥ 12
Since 9 and 12 are ‘like’ terms, we can combine
the two integers so we’re left with zero on the right
side of the equation. We have:
?? + 9 ≥ 12
- 12 ≥ ?12
?? ? 3 ≥ 0

“
Then, since our a term is negative, we
multiply everything by ?1 to make it
positive.
(?1)(?? ? 3) ≥ (0)(?1)
? + 3 ≥ 0

“
Since we multiplied the answer by -1,
the symbol would be changed into ‘≤’.
Hence, we have:
? + 3 ≤ 0
Based on the equation,
a=1, b=3

“
? Let us rewrite the following linear
inequalities in the form ax+ b>0 and
determine the a and b values.
2? ? 1 < 3? + 5
Answer:
? + 6 > 0 a=1, b= 6

1. What is a linear inequality in one variable?
Questions:
2. How can we identify if the expression is written in
standard form?
3. How can we transform ?
1
2
? ? 7 ≥ 5 into standard form?
4. If a=6 and b=7, what would be the standard for of the
linear equation in one variable? How about the linear
inequality in on variable if the inequality symbol is ≥ ?

Group Activity: Determine whether each of the following
situations is a linear inequality or a linear equation in
one variable and write mathematical model that
represents the equation or inequality.
Real-life
Situation
Classification
(Linear Inequality
in one variable or
Linear inequality in
one variable)
Mathematical
model
1. Non-metals
(n)have more than 4
valence electrons.
Linear
inequality in
one variable
? > 4

Real-life Situation
Classification (Linear
Inequality in one
variable or Linear
inequality in one
variable)
Mathematical
model
2. For water to
stay liquid, it
should be less
than 32?F in
temperature (t).
Linear
inequality
in one
variable
? < 32

Real-life Situation
Inequality in one
variable or Linear
inequality in one
variable)
Mathematical
model
3. The maximum
time (t) of
grilling ? kilo of
meat is 8
minutes.
Linear
inequality
in one
variable
? ≤ 8

Real-life Situation
Inequality in one
variable or Linear
inequality in one
variable)
Mathematical
model
4. According to
dieticians, adults
should have no more
than 2.5 tablespoons
(t) of any sugar
added to a food or
drink in a day.
Linear
inequality
in one
variable
? ≤ 2.5

Real-life Situation
Inequality in one
variable or Linear
inequality in one
variable)
Mathematical
model
5. The population
(P) of the
Philippines is
about 103, 000,000
P= 103,000,000
Linear
equation in
one variable

Things to Remember
If an expression relates two
expressions or values with a ‘<’
(less than) sign, ‘>’ (greater than)
sign, ‘≤’ (less than or equal) sign
or ‘≥’ (greater than or equal) sign,
then it is called as an Inequality.

Things to Remember
The steps in rewriting an inequality in one
variable into standard form are as follows:
1. Remove the fraction/s by multiplying each term
by the LCM.
2. Combine ‘like terms’ so what’s left is zero on the
right side of the equation.
3. The a term or the leading coefficient must be
positive. If it is negative, we multiply everything
by ?1 to make it positive.

1.
?
3
= 10
2. 5? + 5 ≥ 19 ? 2?
3. 3? ? 12 ≤ 0
??
?
??

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theme title text
B. Rewrite the following into standard form and
determine the values of a and b.
30
1. ?2? ≥ 11
An?wer

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?????: ?2? ≥ 11
31
2? + 11 ≤ 0

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