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1.4 Solving Inequalities
I can:
1.Graph inequalities
2.Solve inequalities
To Start:
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As with an equation, the solutions of an inequality are
the ______________ that make it true.
An equation, such as 2x = -10 has only one solution,
x = -5. On the other hand, the inequality 2x> -10 is true
for many values of x. Let’s solve that inequality and see
what numbers do make it true.
Example: Solve 2x > -10
Summary: Properties of Inequalities
Let a, b, and c represent real numbers.
Addition Property:
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Subtraction Property:
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Multiplication Property:
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Division Property:
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Solving Inequalities
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Solving inequalities follows the same
procedures as solving equations.
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There are a few special things to
consider with inequalities:
● We need to look carefully at the inequality sign.
● We also need to graph the solution set.
Review of Inequality Signs
> greater than
< less than
 greater than or equal
 less than or equal
How to graph the solutions
> Graph any number greater than. . .
open circle, line to the right
< Graph any number less than. . .
open circle, line to the left
 Graph any number greater than or equal to. . .
closed circle, line to the right
 Graph any number less than or equal to. . .
closed circle, line to the left
Solve the inequality:
x+4<7
-4 -4
x < 3
●Subtract 4 from each side.
●Keep the same inequality sign.
●Graph the solution.
• Open circle, line to the left.
0
3
There is one special case.
● Sometimes you may have to reverse the
direction of the inequality sign!!
● That only happens when you
multiply or divide both sides of the
inequality by a negative number.
Example:
Solve: -3y + 5 >23
●Subtract 5 from each side.
-5 -5
-3y > 18
-3
-3 ●Divide each side by negative 3.
y < -6 ●Reverse the inequality sign.
●Graph the solution.
•Open circle, line to the left.
-6
0
Try these:
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Solve 2x+3>x+5
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Solve - c - 11>23
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Solve 3(r-2)<2r+4
Some inequalities have no solution, and
some are true for all real numbers.
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Example 2: Solve and graph each inequality.
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2x -3> 2(x -5)
Some inequalities have no solution, and
some are true for all real numbers.
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2.
7x + 6 < 7(x - 4)
Try These…
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1.
2x < 2(x +1)
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2.
4(x -3)+7 ³ 4x +1