Properties of absolute inequality

Q. $|-3x+7|>-5$
Which of the following best describes the solutions to the inequality shown above?

1. No solution
2. All the real numbers
3. $x<\frac{7}{3}orx>3$
4. $\frac{7}{3}<x<3$

Q. Solve $\frac{8-3x}{3}\le \frac{2x}{3}-4$

1. $[2,\infty )$
2. $(-\infty ,\infty )$
3. $[4,\infty )$
4. $[5,\infty )$

Q. If $|x|<2$, what are the range of values for x?

1. $x<2$
2. $x<-2$
3. $x<2andx>-2$
4. $x>2andx<-2$

Q.

For a real number x, let [x] denote the largest integer less than or equal to x, and let {x} = x - [x]. The number of solutions x to be equation [x]{x} = 5 with is 0 $\le$ x $\le$ 2015 is

1. 0

2. 3

3. 2008

4. 2009