Kerala Board Solutions for Chapter: Real Numbers, Exercise 2: Exercise 2

Find the value of $x$ satisfying the equation below.

$\left|x\right|=\left|x+1\right|$

Prove that $1<x<4$ and $1<y<4$, then $\left|x-y\right|<3$.

Prove that if $x<3$ and $y>7$, then $\left|x-y\right|>4$.

Find two numbers $x, y$ such that $\left|x+y\right|=\left|x\right|+\left|y\right|$

Are there numbers $x, y$ such that $\left|x+y\right|<\left|x\right|+\left|y\right|?$

Are there numbers  $x, y$ such that $\left|x+y\right|>\left|x\right|+\left|y\right|?$

What are the numbers $x$, for which $|x–2|+|x–8|=6$

What are the numbers $x$, for which $|x–2|+|x–8|=10$