Question

Which point is part of the solution of the inequality y<=|x+4|-3

Answer 1

Hello!

The answer is: The point (0,0) is part of the solution.

Why?

To find which point is part of the solution of the inequality, we need to evaluate each of the given points. If the inequality is satisfied, then the point is part of the solution, otherwise, if the inequality is not satisfied, the point is not part of the solution.

We are given the inequality:

$y\leq |x+4|-3$

So, evaluating we have:

- First point (-2,1)

$y\leq |x+4|-3\\\\1\leq |-2+4|-3\\\\1\leq |2|-3\\\\1\leq 2-3\\\\1\leq -1$

Now, since 1 is not less or equal to -1, the point (-2,1) is not part of the solution.

- Second point (1,3)

$y\leq |x+4|-3\\\\3\leq |1+4|-3\\\\3\leq |5|-3\\\\3\leq 5-3\\\\3\leq 2$

Now, since 3 is not less or equal to 2, the point (1,3) is not part of the solution.

- Third point (-4,2)

$y\leq |x+4|-3\\\\2\leq |-4+4|-3\\\\2\leq |0|-3\\\\2\leq 0-3\\\\2\leq -3$

Now, since 2 is not less or equal to -3, the point (-4,2) is not part of the solution.

- Fourth point (0,0)

$y\leq |x+4|-3\\\\0\leq |0+4|-3\\\\0\leq |4|-3\\\\0\leq 4-3\\\\0\leq 1$

Now, since 0 is less than 1, the point (0,0) is part of the solution.

Hence, we have that the point (0,0) is part of the solution.

Have a nice day!