Boundary line, the shading, and a point in the solution set of the inequality x – 4 ≤ -2(y + 6)?

Question

asked May 24, 2021 132k views

1 Answer

Aeradriel · Answer 1 · 2021-05-27T23:24:15+0000

Answer:

see the explanation

The graph in the attached figure

Explanation:

we have

$x-4\leq -2(y+6)$

isolate the variable y

$x-4\leq -2y-12$

Adds 12 both sides

$x-4+12\leq -2y$

$x+8\leq -2y$

Divide by -2 both sides

Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

$-(x)/(2) -4\geq y$

Rewrite

$y\leq -(x)/(2) -4$

we know that

The solution of the inequality is the shaded area below the solid line

y= -(x)/(2) -4

The slope of the solid line is negative m=-1/2

The y-intercept of the solid line is (0,-4)

The x-intercept of the solid line is (-8,0)

therefore

The graph in the attached figure

A solution of the inequality could be (0,-4)

because the point (0,-4) lie in the shaded area of the solution set