solving rational equations and inequalities objective: use algebra to solve rational inequalities
TRANSCRIPT
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Solving Rational Equations and Inequalities
Objective: Use algebra to solve rational inequalities.
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![Page 5: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/5.jpg)
Example 1
![Page 6: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/6.jpg)
Example 1
![Page 7: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/7.jpg)
Example 1
![Page 8: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/8.jpg)
Example 1
![Page 9: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/9.jpg)
Example 2
![Page 10: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/10.jpg)
Example 2
![Page 11: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/11.jpg)
Example 2
![Page 12: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/12.jpg)
Try This
• Solve2
1
3 x
x
![Page 13: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/13.jpg)
Try This
• Solve2
1
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Try This
• Solve2
1
3 x
x
1,3
0)1)(3(
032
3)2(2
x
xx
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true;1123
1
3
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Extraneous Solutions
• Sometimes solving a rational equation introduces extraneous solutions. An extraneous solution is a solution to a resulting equation that is not a solution to the original equation. Therefore, it is important to check your answers.
![Page 16: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/16.jpg)
Example 3
![Page 17: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/17.jpg)
Example 3
![Page 18: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/18.jpg)
Example 3
![Page 19: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/19.jpg)
Example 3
![Page 20: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/20.jpg)
Try This
• Solve65
3
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![Page 21: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/21.jpg)
Try This
• Solve65
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![Page 22: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/22.jpg)
Try This
• Solve65
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![Page 23: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/23.jpg)
Try This
• Solve65
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![Page 24: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/24.jpg)
Try This
• Solve65
3
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![Page 25: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/25.jpg)
Example 4
![Page 26: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/26.jpg)
Example 4
![Page 27: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/27.jpg)
Example 4
![Page 28: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/28.jpg)
Try This
• Solve 32
1
x
x
![Page 29: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/29.jpg)
Try This
• Solve
• If x+2 > 0, then x > -2
32
1
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2
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x
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![Page 30: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/30.jpg)
Try This
• Solve
• If x+2 > 0, then If x + 2 < 0, then x > -2 x < -2
32
1
x
x
2
72
631
)2(31
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![Page 31: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/31.jpg)
Try This
• Solve 32
1
x
x
2,27 xx
![Page 32: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/32.jpg)
Example 5
![Page 33: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/33.jpg)
Example 5
![Page 34: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/34.jpg)
Example 5
![Page 35: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/35.jpg)
Example 5
![Page 36: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/36.jpg)
![Page 37: Solving Rational Equations and Inequalities Objective: Use algebra to solve rational inequalities](https://reader033.vdocuments.mx/reader033/viewer/2022061305/5513faf6550346e2488b460a/html5/thumbnails/37.jpg)
Homework
• Pages 517-518• 9-27 odd