Solve for $x$: $\left|x\right|\le 3$, where $\left|x\right|$ is modulus function.

Solve for $x$: $2\left|x\right|=5$, where $\left|x\right|$ is modulus function.

Solve for $x$: $[x+[x+\left[x\right]\left]\right]=9$,where $\left[x\right]$ is greatest integer function.

Solve for $x$: $\left\{x\right\}>4$, where $\left\{x\right\}$ is a fractional part function.

Solve for $x$: $\left\{x\right\}=0$, where $\left\{x\right\}$ is a fractional part function.

Solve for $x$: $\left\{x\right\}=0.5$, where $\left\{x\right\}$ is a fractional part function.

Solve for $x$: $2\left\{x\right\}=x+\left[x\right]$, where $\left[x\right]$ is greatest integer function and $\left\{x\right\}$ is a fractional part function.