Transcript 1.6 - BakerMath.org

Solving Inequalities
2 x  5  10
Solving Inequalities
●
Solving inequalities follows the same procedures as
solving equations with 2 new rules.
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The sign (direction) of the inequality changes when:
● You multiply or divide by a negative number
● You swap positions of the variable and answer
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
Properties of Inequalities



Transitive Property
If a  b and b  c, then a  c
Addition Property
If a  b then a + c  b + c
Subtraction Property
If a  b then a –c  b - c

Properties of Inequalities


Multiplication Property
If a < b, and c > 0, then
If a < b, and c < 0, then
Division Property
If a < b, and c > 0, then
If a < b, and c < 0, then
ac < bc
ac > bc
a/c < b/c
a/c > b/c