Download Notes Linear Inequalities

Notes Linear Inequalities
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Recall Inequality symbols:
 less than
 less than or equal to
> greater than
 greater than or equal to
To solve a linear inequality you must isolate the variable on one side of the inequality symbol (like
you do with a linear equation). Your answer is the set of numbers that make the statement true.
Note: When you solve a linear inequality, if you MULTIPLY or DIVIDE by a negative number to solve,
you must FLIP your inequality symbol.
Solve, graph and express your answer in interval notation
EX1: 4 x  5  2 x  1
EX2: 2 x  5x  14
EX3: 3  2 x  5  5
Notes Absolute Value Inequalities
To solve Absolute Value Inequalities
1. ISOLATE the absolute value expression (get absolute value expression alone )
2. Once you isolate the absolute value expression
a. If the number obtained once you isolated is POSITIVE then
i.
If your symbol is  or  you will be sandwiched between the positive and negative of
the number. Rewrite as: neg #  expression with NO abs value bars  pos #
Then, solve your inequality for the variable.
ii.
If your symbol is > or  you will split into 2 different inequality statements. Rewrite as:
expression with NO abs value bars < neg # or expression with NO abs value bars > pos #
Then, solve your inequality for the variable.
b. If the number obtained once your isolated is NEGATIVE then
i.
If your symbol is  or  your answer will be NO SOLUTION because you can never
have a positive number less than a negative number.
ii.
If your symbol is  or  your answer will be ALL REAL NUMBERS because a positive
number is always greater than a negative number.
c. If the number obtained once you isolated is ZERO then
i.
If expression  0 , then drop the absolute value bars, set the expression=0 and solve
for x. Your answer will be all real numbers EXCEPT the answer you obtained.
ii.
If expression  0 , then your answer is ALL REAL NUMBERS.
iii.
If expression  0 , then your answer is NO SOLUTION.
iv.
If expression  0 , then drop the absolute value bars, set the EXPRESSION=0 and solve
for x. Your answer will be ONLY THE NUMBER YOU OBTAINED WHEN YOU SOLVED.
Solve the following inequalities and graph them. Express your answer in interval notation
EX4: x  2
EX5: x  2
EX6: x  0
EX7: 2 x  1  3
EX8: x  8  5
EX9: 3x  7  0
EX10: 2 3x  2  8
EX11: x  7  10  2
EX12: 3 2 x  4  8  10