Solving Linear Inequalities and Compound Inequalities.
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Transcript of Solving Linear Inequalities and Compound Inequalities.
Solving Linear Inequalitiesand
Compound Inequalities
Inequality SymbolsInequality Symbols
is less
than
is greater than
is less than or equal to
is greater than or equal to
is not equal to
Linear Inequality
• Can be written in the form ax+b<0, ax+b>0, ax+b≤0, or ax+b≥0 where a and b are real numbers and a≠0
• Has one variable to the first power.
for example: 2x-3<8
• A solution is a value of the variable that makes the inequality true.
x could equal -3, 0, 1, etc.
Transformations for InequalitiesTransformations for Inequalities
• Add/subtract the same number on each side of an inequality
• Multiply/divide by the same positive number on each side of an inequality
• If you multiply or divide by a negative number, you MUST flip the inequality sign!
Ex: Solve the inequality.
2x-3<8
+3 +3
2x<11
2 2
x<2
11
1373 x
63 x
2x
Flip the sign after dividing by the -3!
Graphing Linear Inequalities
• Remember:
< and > signs will have an open circle
and signs will have a closed circle
graph of graph of
2
11x 2x
4 5 6 7 -3 -2 -1 0
Example: Solve and graph the solution.
121097 xx
1239 xx321x7
6 7 8 9
Example: Solve and graph the solution.
6( 5 3 ) 3(6 10)p p 30 18 18 30p p
18p
30 30
18p
This is a true statement, therefore the solution is ALL REAL NUMBERS.
Compound Inequality
• An inequality joined by “and” or “or”.
Examples
“and”/intersection “or”/union
think between think oars on a boat
13 x
-4 -3 -2 -1 0 1 2
4or 2 xx
-3 -2 -1 0 1 2 3 4 5
Example: Solve & graph.
-9 < t+4 < 10
-4 -4 -4
-13 < t < 6
Think between!
-13 6
Solve & graph. -6x+9 < 3 or -3x-8 > 13
-6x < -6 -3x > 21
x > 1 or x < -7
Flip signs
Think oars
-7 1