Absolute Value or Modulus of a Real Number

Identify on the number line, the points $x$ satisfying $\left|x-2\right|\le 3$

Identify on the number line, the points $x$ satisfying $\left|x\right|>3$

Identify on the number line, the points $x$ satisfying $\left|x\right|\ge 3$

Identify on the number line, the points $x$ satisfying $\left|x\right|<3$

Identify on the number line, the points $x$ satisfying $\left|x\right|\le 3$

If $a^2+b^2=0$, prove that $a=0$ and $b=0$

Find $x$ if $\left|x-2\right|=x$

Find $x$ if $\left|x-3\right|=\sqrt{2}$

Find $x$ if $\left|x-2\right|=3$

Find $x$ if $\left|x-2\right|=0$

Give any three values of $x$ satisfying $\left|x-3\right|<1$.

If $\left|a\right|=\left|b\right|$, find the possible relations between $a$ and $b$.

The operation of division in $R$ is associative.

The operation of subtraction in $R$ is commutative.

The reciprocal of a nonzero rational number is rational.

The set of integers has a multiplicative identity.

The set of natural numbers contains additive identity.

The reciprocal of an irrational number is irrational.