How do you graph the inequality #y - 5 > 2(x - 5)#?
Graph and solve the inequality: y - 5 > 2(x - 5)
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To graph the inequality (y - 5 > 2(x - 5)), you first graph the corresponding equation (y - 5 = 2(x - 5)), then determine which side of the line to shade based on the inequality sign (>).
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Start by graphing the equation (y - 5 = 2(x - 5)).
- First, find the y-intercept by setting (x = 0): (y - 5 = 2(0 - 5)).
- Solve for (y): (y - 5 = -10), so (y = -5).
- Plot the point (0, -5).
- Next, find the x-intercept by setting (y = 0): (0 - 5 = 2(x - 5)).
- Solve for (x): (-5 = 2x - 10), so (2x = 5) and (x = \frac{5}{2}).
- Plot the point ((\frac{5}{2}), 0).
- Draw a straight line passing through these two points.
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Determine which side of the line to shade.
- To do this, pick a test point not on the line, like (0, 0).
- Substitute the test point's coordinates into the original inequality.
- If the inequality is true, shade the side containing the test point; if false, shade the other side.
- For (x = 0) and (y = 0), the inequality becomes (0 - 5 > 2(0 - 5)), which simplifies to (-5 > 10), which is false.
- Therefore, the side of the line that does not contain the point (0, 0) is the solution region.
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Shade the appropriate side of the line to represent the solution to the inequality.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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