Tag: real numbers

Questions Related to real numbers

The value of x on simplifying $x -2 |x|=-3$ is

absolute value real numbers (rational and irrational numbers) real numbers basic algebra maths

  1. -1 or 3

  2. 1 or -3

  3. -1 or -3

  4. 1, 3

Show answer
Correct Option: A
Explanation:

$x-2|x| = -3$

There two cases possible either $x$ is positive or$x$ is negative
We have to solve both cases
Firstly taking x as positive
$x-2x=-3$
$x=3$
Now taking $x$ as negative
$x-2(-x)=-3$
$3x=-3$
$x=-1$
So we get two values of $x$ that is -1 and 3
 So correct answer will be option A

Simplification of $-|-48|$ is

absolute value real numbers (rational and irrational numbers) real numbers basic algebra maths

  1. $48$

  2. $-48$

  3. $0$

  4. $-47$

Show answer
Correct Option: B
Explanation:
Since $|-x| = x$
$-|-48| = -(48) = -48$
So, option $B$ is correct.

If $a$ and $b$ are any real numbers, then which of the following expressions is always positive?

absolute value real numbers (rational and irrational numbers) real numbers basic algebra maths

  1. $\left| a \right| $

  2. $\left| a+b \right| $

  3. $\left| a-b \right| +1/2$

  4. ${ a }^{ 2 }+{ b }^{ 2 }$

  5. ${ \left( a+b \right) }^{ 2 }$

Show answer
Correct Option: C
Explanation:

Lets check each option one by one.

A. |a| cab be 0 if a=0 
B. |a+b| can be 0 if a+b=0
C. |a-b|+ 1/2  will always positive because |a+b| is either 0 or positive 
D. ${a}^{2}+{b}^{2}$ can be 0 if both $a$ and $b$ becomes 0
E ${(a+b)}^{2}$ can equal to 0 if $a+b$ = 0
So correct answer will be option C