How do you graph the inequality #y - 5 > 2(x - 5)#?

Answer 1

Graph and solve the inequality: y - 5 > 2(x - 5)

y - 5 > 2x - 10 y > 2x - 5 (1) First, graph the linear function y = 2x - 5 (2) by its intercepts. Make x = 0, --> y-intercept --> (0, -5) Make y = 0, --> 2x - 5 = 0 --> x-intercept --> #(5/2, 0).# The solution set of the inequality (1) is the whole area above the line (2). Color or shade it, This is the answer. graph{2x - 5 [-10, 10, -5, 5]}
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Answer 2

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 (>).

  1. 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.
  2. 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.
  3. Shade the appropriate side of the line to represent the solution to the inequality.

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Answer from HIX Tutor

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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