Using worldmapper in teaching - discussing inequality in the classroom
1.5 Solving Inequalities. Write each inequality using interval notation, and illustrate each...
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Transcript of 1.5 Solving Inequalities. Write each inequality using interval notation, and illustrate each...
![Page 1: 1.5 Solving Inequalities. Write each inequality using interval notation, and illustrate each inequality using the real number line.](https://reader036.fdocuments.in/reader036/viewer/2022081520/5697bf7b1a28abf838c83698/html5/thumbnails/1.jpg)
1.5 Solving
Inequalities
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A closed interval, denoted by a,b ,
consists of all real numbers x for which a x b.
The half-open, or half closed, intervals are (a,b],
consisting of all real numbers x for which a x b,
and [a,b), consisting of all real numbers x
for which a x b.
An open interval, denoted by a,b ,
consists of all real numbers x for which a x b.
![Page 3: 1.5 Solving Inequalities. Write each inequality using interval notation, and illustrate each inequality using the real number line.](https://reader036.fdocuments.in/reader036/viewer/2022081520/5697bf7b1a28abf838c83698/html5/thumbnails/3.jpg)
An interval, denoted by a, ,
consists of all real numbers x for which x a.
An interval, denoted by a, ,
consists of all real numbers x for which x a.
An interval, denoted by ,a ,
consists of all real numbers x for which x a.
An interval, denoted by ,a ,
consists of all real numbers x for which x a.
![Page 4: 1.5 Solving Inequalities. Write each inequality using interval notation, and illustrate each inequality using the real number line.](https://reader036.fdocuments.in/reader036/viewer/2022081520/5697bf7b1a28abf838c83698/html5/thumbnails/4.jpg)
Write each inequality using interval notation,
and illustrate each inequality using the real
number line.
![Page 5: 1.5 Solving Inequalities. Write each inequality using interval notation, and illustrate each inequality using the real number line.](https://reader036.fdocuments.in/reader036/viewer/2022081520/5697bf7b1a28abf838c83698/html5/thumbnails/5.jpg)
Write each interval as an inequality, and illustrate each inequality using the
real number line.
![Page 6: 1.5 Solving Inequalities. Write each inequality using interval notation, and illustrate each inequality using the real number line.](https://reader036.fdocuments.in/reader036/viewer/2022081520/5697bf7b1a28abf838c83698/html5/thumbnails/6.jpg)
Solving Inequalities 1. Eliminate all fractions by multiplying LCM
2. Use the Distributive Property3. Combine all like terms4. Isolate the variable term5. Divide (Negative – Change
Inequality Sign)6. Write your solution in Interval
Notation7. Graph the inequality on a number
line
![Page 7: 1.5 Solving Inequalities. Write each inequality using interval notation, and illustrate each inequality using the real number line.](https://reader036.fdocuments.in/reader036/viewer/2022081520/5697bf7b1a28abf838c83698/html5/thumbnails/7.jpg)
Solving Inequalities
Reciprocal Property 1
If 4x 3 0,then 4x 3 0.
![Page 8: 1.5 Solving Inequalities. Write each inequality using interval notation, and illustrate each inequality using the real number line.](https://reader036.fdocuments.in/reader036/viewer/2022081520/5697bf7b1a28abf838c83698/html5/thumbnails/8.jpg)
Solve each inequality, and express your answer using
interval notation. Graph each inequality using the
real number line.
2x 3 x11. 2
5 2
10. 3 2x 5
9. 4 x 2 6 18
![Page 9: 1.5 Solving Inequalities. Write each inequality using interval notation, and illustrate each inequality using the real number line.](https://reader036.fdocuments.in/reader036/viewer/2022081520/5697bf7b1a28abf838c83698/html5/thumbnails/9.jpg)
Solve each inequality, and express your answer using
interval notation. Graph each inequality using the
real number line.12. 5 3 2x 7
2x 213. 4 6
3
3 5x14. 1 9
2
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1.6 Absolute
Value Equations
and Inequalities
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Absolute Value Equations
![Page 12: 1.5 Solving Inequalities. Write each inequality using interval notation, and illustrate each inequality using the real number line.](https://reader036.fdocuments.in/reader036/viewer/2022081520/5697bf7b1a28abf838c83698/html5/thumbnails/12.jpg)
1.Isolate the absolute value expression
2.Rewrite the absolute value equation as two separate equations
3.One positive and the other negative
4.Solve each equation and check
Absolute Value Equations
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Solve each equation for the given variable
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Solve each equation for the given variable
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1.Isolate the absolute value expression
2.Write the absolute value inequality as an equivalent conjunction or disjunction
3.Conjunction ( < or < ) AND
4.Disjunction ( > or > ) OR
5.Solve each inequality and graph
Absolute Value Inequalities
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Absolute Value Inequalities
![Page 17: 1.5 Solving Inequalities. Write each inequality using interval notation, and illustrate each inequality using the real number line.](https://reader036.fdocuments.in/reader036/viewer/2022081520/5697bf7b1a28abf838c83698/html5/thumbnails/17.jpg)
Solve each equation for the given variable