Absolute Value Function

Q.

Find the value of |x+b| + |x + a| + |a-b| ___

Q. Match the equations in modulus with their respective solutions

1. x = 0 or x = 8
2. $x=\pm 1$
3. x = -1 or x = 4
4. x=4 or x=-43

Q.

Find the value of |x+b| + |x + a| + |a-b| ___

Q.

Find the value of |x+b| + |x + a| + |a-b| ___

Q. The sum of the solutions of the equation $|\sqrt{x}-2|+\sqrt{x}(\sqrt{x}-4)+2=0,(x>0)$ is equal to:

1. $4$
2. $9$
3. $10$
4. $12$

Q. Set of solutions of the equation $3\left|\right(x-9{)}^2(x-1)|-6|x^2-10x+9|=0$ is

1. $\{1,7,9\}$
2. $\{1,7,9,11\}$
3. $\{1,9,11\}$
4. $\{1,9\}$

Q. If $\left|\frac{2-3|x|}{1+|x|}\right|=1,$ then $x=$

1. $\frac{3}{2}$
2. $-\frac{3}{2}$
3. $-\frac{1}{4}$
4. $\frac{1}{4}$

Q. If $|x-1|+|x-4|=4$, then $x\in$

1. $\{-\frac{1}{2},\frac{9}{2}\}$
2. $\{-\frac{9}{2},-\frac{1}{2}\}$
3. $\{\frac{1}{2},\frac{9}{2}\}$
4. $\{-\frac{9}{2},\frac{1}{2}\}$

Q. The value(s) of $x$ for which $|2x-3|-|x+2|=4$ holds true, is

1. $\{1,9\}$
2. $\{-1,9\}$
3. $\{-1,1\}$
4. $\left\{9\right\}$

Q. If $|4x^2-16x+16|-7|x-2|=-3$, then the value(s) of $x$ is/are

1. $1$
2. $3$
3. $\frac{11}{4}$
4. $\frac{5}{4}$