Question

48. Which is the graph of the solution set of|2x - 1| < 9 ?A. H-5 -4 -3 -2 -1 0 1 2 3 45B.-5 -4 -3 -2 -1 0 1 2 3 4 5C. +-5 -4 -3 -2 -1 01 2 3 4 5D.HH-5 -4 -3 -2 -1 0 1 2 3 4 572-- لا

Answer 1

We have to find the representation of the solution set of the inequality:

$|2x-1|<9$

We can divide this inequality into two, as the absolute value function is like a piecewise function.

We can calculate it in the case that 2x-1 is negative. Then, we can solve it as:

$\begin{gathered} -(2x-1)<9 \\ -2x+1<9 \\ -2x<9-1 \\ -2x<8 \\ x>\frac{8}{-2} \\ x>-4 \end{gathered}$

When 2x-1 is positive, we can solve it as:

$\begin{gathered} 2x-1<9 \\ 2x<9+1 \\ 2x<10 \\ x<\frac{10}{2} \\ x<5 \end{gathered}$

Then, if we combine the two results, the solution set is -4 < x <5 and it represented as Option C.

Answer: Option C.