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How do you graph the inequality #2x + y ≤ 4#?

Answer 1

Isaiah Anthony

See a solution process below:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For: #x = 0#

#(2 * 0) + y = 4#

#0 + y = 4#

#y = 4#

#y = 4# or #(0, )#

For: #x = 2#

#(2 * 2) + y = 4#

#4 + y = 4#

#-color(red)(4) + 4 + y = -color(red)(4) + 4#

#0 + y = 0#

#y = 0# or #(2, 0)#

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality. The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y-4)^2-0.125)((x-2)^2+y^2-0.125)(2x+y-4)=0 [-20, 20, -10, 10]}

Now, we can shade the left side of the line.

graph{(2x+y-4)<=0 [-20, 20, -10, 10]}

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Answer 2

Isaiah Anthony

To graph the inequality 2x + y ≤ 4, first graph the line 2x + y = 4. Then, shade the region below the line, including the line itself. This represents all the points (x, y) that satisfy 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.