How do you graph the linear inequality $- 2 x - 5 y < 10$ $-2x - 5y<10$ ?

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Answer 1 · 2018-03-13T16:18:27

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: $x = 0$ $x = 0$

$(- 2 \cdot 0) - 5 y = 10$ $(-2 * 0) - 5y = 10$

$0 - 5 y = 10$ $0 - 5y = 10$

$- 5 y = 10$ $-5y = 10$

$\frac{- 5 y}{- 5} = \frac{10}{- 5}$ $(-5y)/color(red)(-5) = 10/color(red)(-5)$

$y = - 2$ $y = -2$ or $(0, - 2)$ $(0, -2)$

For: $y = 0$ $y = 0$

$- 2 x - (5 \cdot 0) = 10$ $-2x - (5 * 0) = 10$

$- 2 x - 0 = 10$ $-2x - 0 = 10$

$- 2 x = 10$ $-2x = 10$

$\frac{- 2 x}{- 2} = \frac{10}{- 2}$ $(-2x)/color(red)(-2) = 10/color(red)(-2)$

$x = - 5$ $x = -5$ or $(- 5, 0)$ $(-5, 0)$

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.

graph{(x^2+(y+2)^2-0.05)((x+5)^2+y^2-0.05)(-2x-5y-10)=0 [-10, 10, -5, 5]}

Now, we can shade the rightside of the line.

The boundary line will need to be changed to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(-2x-5y-10) < 0 [-10, 10, -5, 5]}

How do you graph the linear inequality -2x - 5y<10−2x−5y<10-2x - 5y<10?