solve the absolute value equation or indicate that the equation has no solution. |2x - 3| = 9 select the…

solve the absolute value equation or indicate that the equation has no solution. |2x - 3| = 9 select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution set is {}. (simplify your answer. use a comma to separate answers as needed.) b. the solution set is the empty set.

solve the absolute value equation or indicate that the equation has no solution. |2x - 3| = 9 select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution set is {}. (simplify your answer. use a comma to separate answers as needed.) b. the solution set is the empty set.

Answer

Explanation:

Step1: Apply absolute value property

If (|a| = b) ((b\geq0)), then (a = b) or (a=-b). For (|2x - 3| = 9), we have (2x-3 = 9) or (2x - 3=-9).

Step2: Solve (2x-3 = 9)

Add (3) to both sides: (2x=9 + 3), so (2x=12). Divide both sides by (2): (x=\frac{12}{2}=6).

Step3: Solve (2x - 3=-9)

Add (3) to both sides: (2x=-9 + 3), so (2x=-6). Divide both sides by (2): (x=\frac{-6}{2}=-3).

Answer:

A. The solution set is (-3,6)