Question

Which point is NOT part of the solution of the inequality y>= -|x-4|-3

Answer 1

Answer with explanation:

We have to find those points which is not a part of the inequality given

A: (0, 0)

B: (–1, 1)

C: (4, –4)

D: (–3, 2)

⇒The given Inequality is

 y ≥ - | x-4| -3

|x-4|= x-4, when x-4 ≥ 0⇒ x≥ 4

       = - (x-4), when , x-4 ≤ 0⇒ x ≤ 4

The Above Inequality Reduces to

 1. y  ≥ - (x-4) -3 , when , x≥ 4.

        ≥ -x +4 -3

   y ≥ -x +1

2. y ≥ x-4 -3 , when ,  x ≤ 4.

   y ≥ x -7

To plot the inequality,first convert these lines in slope intercept form and then check on which side Origin (0,0) lies.

A. x+y=1

B. x-y=7

After plotting these two lines , put, x=0 and , y=0 in inequality 1,

0 ≥ 1,which is Incorrect.So, shade the region on other side of Origin.

Similarly,  put, x=0 and , y=0 in inequality 2,which gives

0 ≥ -7,,which is Correct. Shade that area on that side on which origin lies.

Plotting the Two Inequality in  two Dimensional Coordinate system, and also Plotting the ordered pairs in the solution set.

Point , (-3, 2) and (-4,4) lies in the solution set.

Other two points, (0,0), and (-1,1)  does not lie in Solution region.

Answer 2

Hello,

0>=-|0-4|-3==>0>=-4-3==>0>=-7 True
1>=-|-1-4|-3==>1>=-5-3==>1>=-8 True
-4>=-|4-4|-3==>-4>=0-3==>-4>=-3 FALSE
2>=-|-3-4|-3==>2>=-7-3==>2>=-10 True

Answer C