linear inequality
DESCRIPTION
Linear Inequality. A linear inequality is any inequality of the form ax + by ≠ c , where the ≠ can be replaced by >, 6. Example 2. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/1.jpg)
A linear inequality is any inequality of the form ax + by ≠ c, where the ≠ can be replaced by >, <, ≥, or ≤.
Linear Inequality
![Page 2: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/2.jpg)
Example 1Graph the solutions to y ≥ −2x + 3. y
x
![Page 3: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/3.jpg)
Check the points (0, 0) and (3, −2) to see if they are solutions to the inequality 2x − 3y > 6.2(0) − 3(0) > 6
0 − 0 > 62(3) − 3(−2) > 6
6 + 6 > 612 > 6
Example 2
![Page 4: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/4.jpg)
y
x
![Page 5: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/5.jpg)
Graph the solutions to y < 4x − 5. y
x
Example 3
![Page 6: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/6.jpg)
Graph y = 4x + 2. Shade with vertical lines the region y > 4x + 2, and shade with horizontal lines the region y < 4x +2.
Example
![Page 7: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/7.jpg)
x
y
![Page 8: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/8.jpg)
Graph y = −2x + 4. Shade with vertical lines the region y > −2x + 4, and shade with horizontal lines the region y < −2x +4.
Example
![Page 9: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/9.jpg)
x
y
![Page 10: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/10.jpg)
Graph 2x + y > 8. Example
![Page 11: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/11.jpg)
x
y
![Page 12: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/12.jpg)
Graph 3x − 4y > 2. Example
![Page 13: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/13.jpg)
x
y
![Page 14: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/14.jpg)
Graph x > 4. Example
![Page 15: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/15.jpg)
x
y
![Page 16: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/16.jpg)
Graph x ≤ −3. Example
![Page 17: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/17.jpg)
x
y
![Page 18: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/18.jpg)
Graph 3x + 4y < 8x − y + 10. Example
![Page 19: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/19.jpg)
x
y
![Page 20: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/20.jpg)
Graph 10(x + 3) ≥ 4(x − y).Example
![Page 21: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/21.jpg)
x
y
![Page 22: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/22.jpg)
Find the solution to y < x + 5 and y > −x + 3. The region below the dashed line through (0, 5) and (−5, 0)
and above the dashed line through (0, 3) and (3, 0)
Example
![Page 23: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/23.jpg)
Graph both of the inequalities in each problem on the same set of axes. Shade the area where the regions overlap darker than the regions where only one of the inequalities is true.
Exercises
![Page 24: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/24.jpg)
y ≤ x + 2 and y > −3x − 1y
x
45
![Page 25: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/25.jpg)
y < x + 3 and y ≤ 2x + 1y
x
−14
![Page 26: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/26.jpg)
3x + y ≥ 5 and − 2x − 3y ≤ 9y
x
![Page 27: Linear Inequality](https://reader036.vdocuments.site/reader036/viewer/2022062501/56815eb8550346895dcd3bd1/html5/thumbnails/27.jpg)
x
y