Question

The difference of 3 times a number and 15 is no less than the square of the number.

Select the inequality that represents this relationship.
A. 3x – 15 > 22
B. 34 < x2 + 15
c. 3x < 32 – 15
D. 3x + 15 > 22

Answer 1

3x - 15 >
`x^(2)`

Explanation:

Let the number be x

⇒3 times the number is 3x and square of the number is
`x^(2)`

Difference of 3 times a number and 15 is 3x -15

⇒This difference is no less than the square of the number

⇒The difference is greater than or equal to square of the number

⇒ 3x - 15 ≥
`x^(2)`

Answer 2

(B) The inequality that represents this relationship is
`3x  < x^2 +15`

Explanation:

Let us assume the given number = x

⇒ 3 times the given number = 3 (x) = 3x

Square of the given number =
`(x)^2  = x^2`

Now, According to the question:

The difference of (3 x) and 15 is no less than
`x^2`

⇒
`3x - 15 < x^2\\ \implies 3x  < x^2 +15`

or,
`3x  < x^2 +15`

Hence, the given inequality is represented as
`3x  < x^2 +15`