Question

Solve the absolute value equation.

|2n + 3| + 19 = 1

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution set is {_} (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

B. The solution set is Ø.​

Answer 1

The absolute value equation |2n + 3| + 19 = 1 has no solution because the absolute value expression is set equal to a negative number, which is not possible.

Step-by-step explanation:

To solve the absolute value equation |2n + 3| + 19 = 1, we first isolate the absolute value expression by subtracting 19 from both sides of the equation:

|2n + 3| = 1 - 19

|2n + 3| = -18

Since the absolute value of a number is always non-negative, there is no number that we can substitute for n to make |2n + 3| equal to -18. Thus, this equation has no solution, and the correct choice is:

B. The solution set is Ø.

When dealing with absolute values, it is important to remember that the expression inside the absolute value brackets can take on negative values, but once the absolute value is applied, the result is always zero or positive. Therefore, an absolute value equation set equal to a negative number does not have a solution.