Modulus Function

Draw the graph of $y=\left|-3x-6\right|$.

Sketch the graph of $y=\left|3x+4\right|$.

Sketch the graph of $y=\left|x+2\right|$.

Solve inequation $1\le \left|x-2\right|\le 3$ in $R$.

Sketch the graphs of the function $y=\left|x+1\right|+2$.

Draw the graph of $y=|x-3|+2$ for $0⩽x⩽6.$ Write the vertex and $y-$intercept.

Solve the following system of inequations: $|x-1|\le 5, \left|x\right|\ge 2$

$N$ is a point on either of two lines $y-\left|x\right|=5$ at a distance of $2$ units from their point of intersection. If the coordinate of the foot of perpendicular from $N$ on the angle bisector between them is $\left(a,b\right)$, then value of $\left|a+b-\sqrt{2}\right|$ is

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

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

Consider the equation ${\int }_0^x\left(t^2-8t+13\right)dt=x\sin \left(\frac{a}{x}\right)$ One of the solutions of $\left|y-\cos a\right|<x$, where $x$ and $a$ are values that satisfy the given equation, is

If $z_1, z_2$ and $z_3$ are $3$ distinct complex numbers such that $\frac{3}{\left|z_1-z_2\right|}=\frac{5}{\left|z_2-z_3\right|}=\frac{7}{\left|z_3-z_1\right|}$, then the value of $\frac{9}{z_1-z_2}+\frac{25}{z_2-z_3}+\frac{49}{z_3-z_1}$ is equal to

If the solution set of $\left|{\sin }^{2}x+17-x^2\right|=\left|16-x^2\right|+2{\sin }^{2}x+{\cos }^{2}x$ contains $n$ integers, then the value of $\frac{111}{n}$ is:

If the smallest integral value of $k$ is equal to $n$ for which the equation $|\mathrm{x}+2|-|\mathrm{x}+1|+|\mathrm{x}-1|=\mathrm{k}, \mathrm{x}\in \mathrm{R}$ has two solution, then $\frac{71}{n}$ equal to.

Area of quadrilateral formed by lines $\left|2x\right| + \left|3y\right| = 2$ is $\left(\frac{k+1}{k}\right)$ then k equals 

Area of quadrilateral formed by lines |2x| + |3y| = 2 is $\left(\frac{k+1}{k}\right)$ then k equals________

The domain of the function $f\left(x\right)=\frac{1}{\sqrt{\left|\mathrm{t}\mathrm{a}\mathrm{n}x\right|-\mathrm{t}\mathrm{a}\mathrm{n}x}}$ is

The number of solution(s) the equation $\left| x – 1\right| + \left|x – 2\right|+\left|x – 3\right|+\left|x – 4\right|= 3$ is 

The number of solution(s) the equation $\left|x-1\right|+\left|x-2\right|+\left|x-3\right|+\left|x-4\right|=3$ is

The function $f\left(x\right)=\left|px-q\right|+r\left|x\right|, x\in (-\infty , \infty )$, where $p>0, q>0, r>0$ assume its minimum value only at one point if