Question

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

Answer 1

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