How do you graph the system of linear inequalities #4x>y# and #x<=12#?
graph{(4x-y)(12-x)^.5>0 [-156.6, 163.4, -91.5, 68.5]}
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Plot the two lines using calculated values.
The first one should have a dotted line along the y = 4x line, as the exact solution is not included. Shade the area below the line. The second one is just a solid line at x = 12 and shading on the left side of it.
The intersection of the two solutions is the common overlapping shaded area.
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To graph the system of linear inequalities 4x > y and x ≤ 12, you would first graph the boundary lines for each inequality separately.
For 4x > y, the boundary line is the line 4x = y, but it's a dashed line because it does not include the points on the line.
For x ≤ 12, the boundary line is the vertical line x = 12, and it's a solid line because it includes the points on the line.
After graphing the boundary lines, shade the region that satisfies both inequalities. In this case, it's the region below the dashed line 4x > y and to the left of the solid line x = 12.
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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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