Final answer:
To solve the absolute value equation |j-5|=|j+9|, we set up two cases and find that the solution is j = -2 after eliminating the first case with no solution and simplifying the second case.
Step-by-step explanation:
To solve the equation |j-5|=|j+9|, we consider two cases because absolute value equations can have two solutions. The inside of the absolute value can be positive or negative, and the number becomes positive after taking the absolute value.
Case 1: If the inside quantities are equal, we can remove the absolute value bars and set the insides equal to each other.
j - 5 = j + 9
Subtract j from both sides: -5 = 9
This equation yields no solution because -5 does not equal 9.
Case 2: If the inside quantities are opposite of each other, we set them equal after multiplying one side by -1 before removing the absolute values.
j - 5 = -(j + 9)
Distribute the negative: j - 5 = -j - 9
Add j to both sides: 2j - 5 = -9
Add 5 to both sides: 2j = -4
Divide by 2: j = -2
Thus, the solution to the equation is j = -2, which is option d.