Question

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Answer 1

Answer:

Correct answer:  F. graph F or x ∈  |-5 ; 5| (including endpoints)

Step-by-step explanation:

Let us first define the absolute value:

| x |  = 1. { x with condition x ≥ 0 }

    or 2. { - x with condition x < 0 }

This is a linear inequality

1.  x ≤ 5  ∧  x ≥ 0   ⇒   0 ≤ x ≤ 5  or interval x ∈  |0 ; 5| (including endpoints)

2. - x ≤ 5  when we multiply both sides of the equation by -1 we get:

x ≥ -5 ∧ x < 0  ⇒  -5  ≤ x < 0 or interval x ∈  |-5 ; 0) (including -5)

The solution to this linear inequality is the union of these two intervals:

x ∈  |-5 ; 0) ∪ |0 ; 5|  ⇒ x ∈ |-5 ; 5| (including endpoints)

x ∈ |-5 ; 5| (including endpoints)

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