Question

Twice a number n is no less than 10 units from −1.

Answer 1

• n ≥ 4.5 or n ≤ - 5.5

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Twice a number n is no less than 10 units from −1:

• Twice a number n ⇒ 2n,
• no less than ⇒ ≥,
• 10 units from −1 ⇒ - 1 ± 10.

The inequality becomes an absolute value and translates as:

• " The difference of 2n and - 1 is equal or greater than 10"

• | 2n - (-1) | ≥ 10
• | 2n + 1 | ≥ 10
• 2n + 1 ≥ 10 or 2n + 1 ≤ - 10
• 2n ≥ 10 - 1 or 2n ≤ - 10 - 1
• 2n ≥ 9 or 2n ≤ - 11
• n ≥ 4.5 or n ≤ - 5.5