Linear inequalities
1. Inequalities of the form \( x > a \)
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In other words, any value of “x” that is larger than “a” would satisfy this inequality. |
Example:
If we have “a = 3”, then the inequality “x > 3” would mean that any value of “x” that is greater than 3, such as 4, 5, 6, and so on, would satisfy the inequality.
Graphically, if you were to plot this inequality on a number line, you would shade the region to the right of the point representing “a”, indicating all the values of “x” that are greater than “a”.
Interactive graph
Use the sliders to adjust the parameters to understand the transformation.
2. Inequalities of the form \( x \geq a \)
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In other words, any value of “x” that is greater than or equal to “a” would satisfy this inequality.
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Example:
If we have “a = 3”, then the inequality \(x \geq 3 \) would mean that any value of “x” that is greater than or equal to 3, such as 3, 4, 5, 6, and so on, would satisfy the inequality.
Graphically, if you were to plot this inequality on a number line, you would shade the region starting from the point representing “a” and extending to the right, indicating all the values of “x” that are greater than or equal to “a”.
Interactive graph
Use the sliders to adjust the parameters to understand the transformation.
3. Inequalities of the form \( x <a \)
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In other words, any value of “x” that is smaller than “a” would satisfy this inequality.
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Example:
If we have “a = 5”, then the inequality “x < 5” would mean that any value of “x” that is less than 5, such as 4, 3, 2, and so on, would satisfy the inequality.
Graphically, if you were to plot this inequality on a number line, you would shade the region to the left of the point representing “a”, indicating all the values of “x” that are less than “a”.
Interactive graph
Use the sliders to adjust the parameters to understand the transformation.
4. Inequalities of the form \( y > b \)
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In other words, any value of “y” that is larger than “b” would satisfy this inequality.
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Example:
If we have “b = 2”, then the inequality “y > 2” would mean that any value of “y” that is greater than 2, such as 3, 4, 5, and so on, would satisfy the inequality.
Graphically, if you were to plot this inequality on a coordinate plane, you would shade the region above the horizontal line corresponding to “y = b”, indicating all the points with “y” values greater than “b”.
Interactive graph
Use the sliders to adjust the parameters to understand the transformation.
5. Inequalities of the form \( y\leq b\)
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In other words, any value of “y” that is smaller than or equal to “b” would satisfy this inequality.
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Example:
If we have “b = 8”, then the inequality “y <= 8” would mean that any value of “y” that is less than or equal to 8, such as 7, 6, 5, and so on, would satisfy the inequality.
Graphically, if you were to plot this inequality on a coordinate plane, you would shade the region below the horizontal line corresponding to “y = b”, indicating all the points with “y” values less than or equal to “b”.
Interactive graph
Use the sliders to adjust the parameters to understand the transformation.