Question

Which of the following inequalities is not true? |-9| ≠ |9| -2 ^2 < 3 -7 ≤ -5 |-1| ≥ 0

Answer 1

|-9| ≠ |9| is not true

Explanation:

A

Answer 2

(a) |-9| ≠ |9| is NOT TRUE.

(b)
`-2 ^2< 3` is TRUE

(c) -7 ≤ -5 is TRUE

(d) |-1| ≥ 0 is TRUE.

Explanation:

Solving each expression separably:

(a) |-9| ≠ |9|

By the definition of MODULUS FUNCTION: IxI = x, if x > 0

= (-x) if x <, 0

⇒ I-9I = -(-9) = 9, and I9I = 9

So, I-9I = I9I . Hence, |-9| ≠ |9| is NOT TRUE.

(b)
`-2 ^2< 3`

⇒
`-2 ^2 = (-2) * (-2) * (-2)  = -8`

and (-8) < 3.

Hence,
`-2 ^2< 3` is TRUE

(c) -7 ≤ -5

-7 < -5 on the number line of integers.

Hence, -7 ≤ -5 is TRUE

(d) |-1| ≥ 0

I(-1)I = -(-1) = 1

and 1 > 0

Hence, |-1| ≥ 0 is TRUE.