Absolute value equations and inequalities

Assuming $x\in [\frac{1}{2};\mathrm{\infty })$, write the following equation in the form which does not contain an absolute value. $$|x+1|+|2x-1|=3$$

Consider the following equation. $$|2x-4|=5x-7$$ Solving the equation on the intervals where it is possible to evaluate the absolute value we get equations on partial subintervals as follows. $$\begin{array}{rlrlrlrl}\text{for }x& \in (-\mathrm{\infty };2):& \text{for }x& \in [2;\mathrm{\infty }):& & & & \\ -2x+4& =5x-7& 2x-4& =5x-7& & & & \\ -7x& =-11& -3x& =-3& & & & \\ x& =\frac{11}{7}& x& =1& & & & \end{array}$$ Find the solution set of the original equation.

Identify the solution set of the following inequality. $$|2x-1|>5$$

Identify the solution set of the following inequality. $$|x|\ge 5$$