The set A satisfying the given inequality is A = (-
, -10].
<h3>What are some properties of an inequality relation? </h3>
Following are some facts which are true for an inequality relation:
- Equal numbers can be added or subtracted from both sides of an inequality without affecting the inequality sign.
- The Inequality sign is unchanged if both sides are multiplied or divided by a positive number, but when multiplied or divided by a negative number the inequality sign is reversed.

Since y ∈ B, -2 ≤ y ≤ 7. So,

The set {-x | inequality (1) holds ∀ y ∈ B} is [10,
) i.e.
10 ≤ -x ≤
.
Multiplying -1 throughout gives
-10 ≥ x ≥ -
.
x, thus, lies in the range A = (-
, -10}.
Learn more about the inequality here.
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<h3>Question </h3>
Find the set A such that for x ∈ A

∀y ∈ B = {y ∈ R | -2 ≤ y ≤ 7}.
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