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Chapter 6 – Solving and
Graphing Linear Inequalities
6.1 – Solving One-Step Linear
Inequalities
6.1 – Solving One-Step Linear
Inequalities
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Today we will learn how to:
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Graph linear inequalities in one variable
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Solve one-step linear inequalities
Vocabulary
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An equation is formed when an equal sign (=) is
placed between two expressions creating a left and
a right side of the equation
An equation that contains one or more variables is
called an open sentence
When a variable in a single-variable equation is
replaced by a number the resulting statement can be
true or false
If the statement is true, the number is a solution of
an equation
Substituting a number for a variable in an equation
to see whether the resulting statement is true or
false is called checking a possible solution
Inequalities
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Another type of open sentence is
called an inequality.
An inequality is formed when and
inequality sign is placed between two
expressions
A solution to an inequality are
numbers that produce a true
statement when substituted for the
variable in the inequality
Inequality Symbols
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Listed below are the 4 inequality
symbols and their meaning
<
Less than
≤
Less than or equal to
>
Greater than
≥
Greater than or equal to
Note: We will be working with inequalities
throughout this course…and you are expected to
know the difference between equalities and
inequalities
Graphs of linear inequalities
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Graph (1 variable)
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The set of points on a number line that
represents all solutions of the inequality
6.1 – Solving One-Step Linear
Inequalities
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Verbal Phrase
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All real numbers
less than 2
All real numbers
greater than -2
All real numbers
less than or equal
to 1
All real numbers
greater than or
equal to 0
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Inequality
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x<2
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x > -2
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x≤1
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x≥0
6.1 – Solving One-Step Linear
Inequalities
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An open dot is used for < and >
A closed dot is used for ≤ and ≥
6.1 – Solving One-Step Linear
Inequalities
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Example 1
Abu was sure he didn’t score less than
a 73 on his algebra test. Write and
graph an inequality to describe Abu’s
possible score.
X ≥ 73
6.1 – Solving One-Step Linear
Inequalities
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Solving a linear inequality in one
variable is much like solving a linear
equation in one variable.
To solve the inequality, you get the
variable on one side using inverse
operations.
6.1 – Solving One-Step Linear
Inequalities
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Transformations that produce
equivalent inequalities
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Add the same number to each side
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x–3<5
Subtract the same number from each
side
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x + 6 ≥ 10
6.1 – Solving One-Step Linear
Inequalities
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Example 2
Solve x + 8 ≥ 1. Graph the solution.
6.1 – Solving One-Step Linear
Inequalities
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Example 3
Solve 3 < m – 5. Graph the solution.
6.1 – Solving One-Step Linear
Inequalities
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USING MULTIPLICATION AND DIVISION
The operations used to solve linear
inequalities are similar to those used to
solve linear equations, but there are
important differences.
When you multiply or divide each side of an
inequality by a negative number, you must
reverse the inequality symbol to maintain a
true statement. For instance, to reverse >,
replace it with <.
6.1 – Solving One-Step Linear
Inequalities
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Transformations that produce
equivalent inequalities
Multiply each side by the same
positive number
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½x>3
Divide each side by the same positive
number
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3x ≤ 9
6.1 – Solving One-Step Linear
Inequalities
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Transformations that produce
equivalent inequalities
Multiply each side by the same
negative number and reverse the sign
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-x < 4
Divide each side by the same negative
number and reverse the sign
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-2x ≤ 6
6.1 – Solving One-Step Linear
Inequalities
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Example 4
Solve the inequality and graph the solution.
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-2.5y > 3
Y < -1.2
p
 2
2
P ≤ -4
6.1 – Solving One-Step Linear
Inequalities
HOMEWORK
Page 337-338
#22 – 54 even