Question

Graph the inequality y<=-|x-4|. which point is NOT part of the solution?

1. (1, -4)
2.(2, -2)
3.(1, 1)
4. 3, -1)

Answer 1

I’m not 100% sure but I think the answer will be number 4. 3 -1 I’m sorry if I’m wrong but in the other hand I hope I helped you and good luck

Answer 2

3. (1,1)

Explanation:

We are given the inequality
`y\leq -|x-4|`.

Upon simplifying the inequality, we have,

`y\leq -|x-4|\\\\y\leq -(x-4),\ y\leq x-4\\\\y\leq -x+4,\ y\leq x-4`

Thus, the inequalities obtained are given by,

`y\leq -x+4\\\\y\leq x-4`

Using 'Zero Test' which states that 'If after substituting (0,00 in the inequalities the result is true, then the solution region is towards the origin and if the result is false, the solution region is towards the origin'.

We have,

`y\leq -x+4` implies 0 ≤ 4, which is true

`y\leq x-4` implies 0 ≤ -4, which is false.

So, the solution region of
`y\leq -x+4` and
`y\leq x-4` are towards the origin and away from the origin respectively as shown below.

After plotting the points in the options, we see that,

Except (1,1), all the other points lie in the solution region.

So, the point which is not the part of the solution is (1,1).