Question

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

Answer 1

Answer:

|-9| ≠ |9| is not true

Step-by-step explanation:

A

Answer 2

Answer:

(a) |-9| ≠ |9| is NOT TRUE.

(b) $-2 ^2< 3$   is TRUE

(c)  -7 ≤ -5 is TRUE

(d) |-1| ≥ 0 is TRUE.

Step-by-step 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) $-2 ^2< 3$  

⇒$-2 ^2 = (-2) \times (-2) \times (-2) = -8$  

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.