Question

*PLEASE ANSWER* // *CONFUSED*

Which type of compound inequality is |y−3|−4≤−3?
a.) disjunction

b.) intersection

c.) hole

d.) union

Answer 1

intersection is right

Explanation:

Answer 2

b.) intersection

Explanation:

The given inequality can be rearranged so that you can see the solution space is one continuous interval.

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It is described by the intersection of two inequalities.

|y -3| -4 ≤ -3 . . . . . . given

|y -3| ≤ 1 . . . . . . . . add 4

-1 ≤ y -3 ≤ 1 . . . . . "unfolded", the intersection of two inequalities

2 ≤ y ≤ 4 . . . . . . . add 3

This means 2 ≤ y and y ≤ 4, the intersection of the two inequalities.

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Additional comment

If the inequality were of the form ...

|y -3| ≥ 1

then it would "unfold" to ...

-1 ≥ y -3 or y -3 ≥ 1

and the solution intervals would be disjoint. The solution would be the union of the solution intervals of the individual inequalities.