solving absolute value inequalities. when you have: less than (< or ≤):we write it as a...
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Solving Absolute Value Inequalities
Solving Absolute Value Inequalities• when you have:• less than (< or ≤): we write it as a “sandwich”
|x + 1|< 3-3 < x + 1 < 3
• greater than (> or ≥): we write it as an “or”|x + 1| > 3
x + 1 > 3 or x + 1 < -3
• Remember as:– less “and”– great “or”
Solving Absolute Value Inequalities
• Isolate the absolute value first– (get it by itself)
• make it an “and” or an “or” statement
• solve and graph
Example
|x| ≥ 6
Example
|x| ≤ 0.5
Example
|x - 5| ≥ 7
Example
|-4x - 5| + 3 < 9
Example
3|5m - 6| - 8 ≤ 13
Solving Inequalities
• one-step and multi-step inequalities– follow the steps for solving an equation– reverse the inequality symbol when
multiplying/dividing by a negative number
• compound inequalities– rewrite as two separate inequalities, if necessary
• absolute value inequalities– isolate the absolute value expression on one side of
the inequality– rewrite as a compound inequality, then solve
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