Absolute Value

Solve $\left|x-2\right|\ge 7, x\in R$

If the solution of the inequality: $\left|x-10\right|>5$ is $x\in (-\infty ,k)\cup (15,\infty )$, then find value of $k$.

Solve the inequality for $x$: $|x+3|\le 7$.

If the solution of the inequality: $\left|x-10\right|>5$ is $x\in (-\infty ,k)\cup (15,\infty )$, then find value of $k$.

Solve the inequality for $x$: $\left|x-8\right|>3$.

If $\mathrm{x}+\left|\mathrm{y}\right|=2\mathrm{y}$ , then $\mathrm{y}$ as a function of $\mathrm{x}$ is

Let $f\left(x\right)=x^2-5x+6, g\left(x\right)=f\left(\right|x\left|\right), h\left(x\right)=\left|g\right(x\left)\right| \mathrm{and} \varphi \left(x\right)=h\left(x\right)-\left(x\right)$ are four functions, where $\left(x\right)$ is the integral function of $x\ge x$. Then, the number of solutions of the equation, $g\left(x\right)=0$ is