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# 3 1 linear inequalities, absolute value

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### 3 1 linear inequalities, absolute value

1. 1. Ch. 3 – Inequalities 3.1 Linear Inequalities; Absolute Value Objectives: Solve and graph linear inequalities in one variable
2. 2. Solving Inequalities • Solve just like an equation, EXCEPT: • The inequality sign must be reversed if you multiply or divide by a negative number Graphing solutions • On a number line: • < , > use open circle •  ,  use closed circle • Shade (or use an arrow) to indicate solution set.
3. 3. Example 1a • Solve 3x – 4  10 + x and graph the solution.
4. 4. Example 1b • Solve and graph the solution.
5. 5. You Try! • Solve and graph the solution.
6. 6. Absolute Value • |x| means (geometrically) the distance from x to zero on the number line. (c  0) Sentence Meaning The distance from x to 0 is: Graph Solution |x| = c exactly c units x = c or x = -c -c 0 c |x| < c less than c units -c < x< c |x| > c greater than c units x < -c or x > c -c 0 c -c 0 c
7. 7. • Sentences with |x – k| can mean the distance from x to k on the number line. Sentence Meaning Graph Solution |x - 5| = 3 The distance from x to 5 is 3 units x = 2 or x = 8 |x - 1| < 2 The distance from x to 1 is less than 2 units -1 < x< 3 |x + 3| > 2 or |x – (-3)| > 2 The distance from x to -3 is greater than 2 units x < -5 or x > -1
8. 8. Algebraic Method Sentence Equivalent Sentence |ax + b| = c ax + b = c |ax + b| < c -c < ax + b < c |ax + b| > c ax + b < -c or ax + b > c
9. 9. Example 2a • Solve |3x – 9| > 4 and graph the solution.
10. 10. Example 2b • Solve |2x + 5|  7 and graph the solution.
11. 11. You Try! • Solve and graph the solution: • |2x + 3 | = 1 • |x – 2|  3