Clear the parentheses using distribution Combine variable terms To keep from having to multiply or...
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![Page 1: Clear the parentheses using distribution Combine variable terms To keep from having to multiply or divide by a negative number, make sure the.](https://reader035.fdocuments.in/reader035/viewer/2022062223/5a4d1b5f7f8b9ab0599ac93b/html5/thumbnails/1.jpg)
Solving Inequalities
![Page 2: Clear the parentheses using distribution Combine variable terms To keep from having to multiply or divide by a negative number, make sure the.](https://reader035.fdocuments.in/reader035/viewer/2022062223/5a4d1b5f7f8b9ab0599ac93b/html5/thumbnails/2.jpg)
Clear the parentheses using distribution Combine variable terms
To keep from having to multiply or divide by a negative number, make sure the final variable term has a positive coefficient
Add/subtract to get constant term isolated Multiply/divide to isolate the variable
If you multiply or divide by a negative number, you must flip the inequality sign
Inequalities are solved for x using the same steps as equations.
![Page 3: Clear the parentheses using distribution Combine variable terms To keep from having to multiply or divide by a negative number, make sure the.](https://reader035.fdocuments.in/reader035/viewer/2022062223/5a4d1b5f7f8b9ab0599ac93b/html5/thumbnails/3.jpg)
For final numeric solutions to match the direction
of the graphic solution, the variable should be on the left side of the inequality.
‘Flip’ the inequality if needed, but make sure to keep the correct order of the inequality.
Inequalities are solved for x using the same steps as equations.
![Page 4: Clear the parentheses using distribution Combine variable terms To keep from having to multiply or divide by a negative number, make sure the.](https://reader035.fdocuments.in/reader035/viewer/2022062223/5a4d1b5f7f8b9ab0599ac93b/html5/thumbnails/4.jpg)
Solutions can be written:
Verbally x greater than three
Symbolically x > 3
Graphically .
Inequalities are solved for x using the same steps as equations.
![Page 5: Clear the parentheses using distribution Combine variable terms To keep from having to multiply or divide by a negative number, make sure the.](https://reader035.fdocuments.in/reader035/viewer/2022062223/5a4d1b5f7f8b9ab0599ac93b/html5/thumbnails/5.jpg)
More Examples
![Page 6: Clear the parentheses using distribution Combine variable terms To keep from having to multiply or divide by a negative number, make sure the.](https://reader035.fdocuments.in/reader035/viewer/2022062223/5a4d1b5f7f8b9ab0599ac93b/html5/thumbnails/6.jpg)
(double back R) means all real numbers are a
solution. Shown graphically
Symbols used in Special Cases
⟷ means no solution (no numbers cause the
statement to be true) No graph, since no numbers work
![Page 7: Clear the parentheses using distribution Combine variable terms To keep from having to multiply or divide by a negative number, make sure the.](https://reader035.fdocuments.in/reader035/viewer/2022062223/5a4d1b5f7f8b9ab0599ac93b/html5/thumbnails/7.jpg)
![Page 8: Clear the parentheses using distribution Combine variable terms To keep from having to multiply or divide by a negative number, make sure the.](https://reader035.fdocuments.in/reader035/viewer/2022062223/5a4d1b5f7f8b9ab0599ac93b/html5/thumbnails/8.jpg)
![Page 9: Clear the parentheses using distribution Combine variable terms To keep from having to multiply or divide by a negative number, make sure the.](https://reader035.fdocuments.in/reader035/viewer/2022062223/5a4d1b5f7f8b9ab0599ac93b/html5/thumbnails/9.jpg)
![Page 10: Clear the parentheses using distribution Combine variable terms To keep from having to multiply or divide by a negative number, make sure the.](https://reader035.fdocuments.in/reader035/viewer/2022062223/5a4d1b5f7f8b9ab0599ac93b/html5/thumbnails/10.jpg)
![Page 11: Clear the parentheses using distribution Combine variable terms To keep from having to multiply or divide by a negative number, make sure the.](https://reader035.fdocuments.in/reader035/viewer/2022062223/5a4d1b5f7f8b9ab0599ac93b/html5/thumbnails/11.jpg)