Graphing and Solving Inequalities

Graphing and Solving Inequalities
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This slide discusses graphing and solving inequalities, with Example 1 demonstrating how to graph inequalities based on verbal phrases and Example 2 showing how to solve an inequality and graph its solution.

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PowerPoint presentation about 'Graphing and Solving Inequalities'. This presentation describes the topic on This slide discusses graphing and solving inequalities, with Example 1 demonstrating how to graph inequalities based on verbal phrases and Example 2 showing how to solve an inequality and graph its solution.. The key topics included in this slideshow are . Download this presentation absolutely free.

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Slide1Graphing InequalitiesEXAMPLE 1 Inequality Graph Verbal Phrase a.      y   <  7 b.     q     3 c.     x  > –5 d.     h     2 1 2 All numbers less than  7 All numbers less than or equal to  3 All numbers greater than  – 5 All numbers greater than or equal to  2 1 2

Slide2Solving InequalitiesEXAMPLE 2 Solve the inequality. Then graph its solution. x  –  5  + 5   < 8  + 5 x  < 13 Original inequality Add  5  to each side. Simplify. x  – 5 < 8 a. x  – 5 < 8

Slide3Solving InequalitiesEXAMPLE 2 y  – 7    –10 y  –  7  + 7      –  10  + 7 y    –3 Original inequality Add  7  to each side. Simplify. b.     y  – 7    –10

Slide4Solving InequalitiesEXAMPLE 2 8   +  m  > 15 8  –  8   +  m  >   15  –  8 m  > 7 Original inequality Subtract  8  from each side. Simplify. c.     8   +  m  > 15

Slide5GUIDED PRACTICEfor Examples 1 and 2 Graph and write a verbal phrase for the inequality. 1.     z  ≥ –1 SOLUTION Inequality Graph Verbal Phrase z  ≥ –1 All numbers greater than or equal to  –1 –3     –2     –1      0      1

Slide6GUIDED PRACTICEfor Examples 1 and 2 2.     4   >  p SOLUTION Inequality Graph Verbal Phrase 4   >  p All numbers less than  4 .   2      3       4       5      6

Slide7GUIDED PRACTICEfor Examples 1 and 2 3.     k    –3.5 SOLUTION Inequality Graph Verbal Phrase k    –3.5 All numbers less than or equal to  –3.5 . –5     –4     –3     –2     –1

Slide8GUIDED PRACTICEfor Examples 1 and 2 4.     m  > 1 2 SOLUTION Inequality Graph Verbal Phrase 1 2 m  > All numbers greater than      . 1 2 –2     –1     0        1      2

Slide9GUIDED PRACTICEfor Examples 1 and 2 5.      x  – 3 > –2 SOLUTION Original inequality Add  3  to each side. Simplify. x  – 3 > – 2 x  –  3 + 3 >   –  2 + 3 x >  1 Graph

Slide10GUIDED PRACTICEfor Examples 1 and 2 6.     6 >  t  – 1 SOLUTION Original inequality Add  1  to each side. Simplify. 6 >  t  – 1 6 + 1 >  t  – 1 + 1 7 > t Graph

Slide11GUIDED PRACTICEfor Examples 1 and 2 7.     12 ≥  p  + 14 SOLUTION Original inequality Subtract  14  from each side. Simplify. 12 ≥  p  + 14 – 14 ≥  p  + 14 12 – 14 ≥  p –2 Graph

Slide12GUIDED PRACTICEfor Examples 1 and 2 8.      x  + 5 < 10 SOLUTION Original inequality Subtract  5  from each side. Simplify. x  + 5 < 10 x  + 5 < 10 – 5 –5 x < 5 Graph x   <  5 3      4       5       6      7

Slide13GUIDED PRACTICEfor Examples 1 and 2 9.      t  + 9    6 SOLUTION Original inequality Subtract  9  from each side. Simplify. t  + 9    6 t  + 9 – 9   6 – 9  –3 t Graph

Slide14GUIDED PRACTICEfor Examples 1 and 2 10.     –4 <  k  –3 SOLUTION Original inequality Add 3 to each side. Simplify. –4  <  k   – 3 <  k  – 3 + 3 –4 + 3 <  k –1 Graph