Application of inequalities and absolute values

Q. Solve the absolute value inequality $2\times |3x+9|<36$

1. - 9 > x > 3
2. - 9 < x < 3
3. x > - 9
4. x < 3

Q. $4|6+2x|-27\le -3$ which of the following best describes the solutions to the inequality shown above ?

1. $-24\le x\le 0$
2. $-6\le x\le 0$
3. No solution
4. $x\le 0orx\ge 3$

Q. Let $f\left(x\right)=x^3-3x+4b$ and $g\left(x\right)=x^2+bx-3$ where, b is a real number. If the equations $f\left(x\right)=0$ and $g\left(x\right)=0$ have a common root, then

1. number of possible values of $b$ is $3$
2. number of possible values of $b$ is $2$
3. sum of all possible values of $b$ is $0$
4. sum of all possible values of $b$ is $1$

Q.

If the conjugate of (x+iy)(1-2i) be 1+i, then

1. 

2. 

3. 

4. 

Q. $|2x+3y|<15$ What is the range of values for y, expressed in terms of x?

1. $y>15-12x$
2. $-5-4x<y<5-4x$
3. $5-4x<y<5+4x$
4. $5+4x<y<5-4x$

Q. $|4x+14|>30$ what is a possible valid value of x?

1. 7
2. 1
3. - 11
4. - 3

Q.

If $|x-5|+|x-10|⩽20$, then x belongs to

1. [2.5, 17.5]

2. [-2.5, 17.5]

3. [-7.5, 2.5]

4. [-17.5, 2.5]

Q. Solve for x. $|5x-75|>45-x$

1. $x>7.5$
2. $x>20$
3. $-20<x<-7.5$
4. $x>7.5,x>20$

Q. How do you solve $\frac{x}{2}+\frac{x}{4}=5?$

Q. Let $p,q,r\in R^{+}$ such that $27pqr\ge (p+q+r{)}^3$ and $3p+4q+5r=12.$ Then the value of $p+q+r$ is

1. $3$
2. $6$
3. $2$
4. $12$

Q. Solve the following inequality:
$|x-6|>|x^2-5x+9|.$

Q. Solve the following inequality:
$\frac{19-33x}{7x^2-11x+4}>2$

Q. Solve the following inequalities. $\frac{b+3}{5-2b}\le 4$ where $b\le \frac{17}{a}$ then find $a$.