Answer: the equation j = 2j + 3 has two solutions: j = -3 and j = -3.
Step-by-step explanation: To make the equation j = 2j + 3 have two solutions, we need to find values of j that satisfy the equation.
To do this, let's start by simplifying the equation:
j = 2j + 3
To get rid of the 2j term on the right side of the equation, we can subtract 2j from both sides:
j - 2j = 2j - 2j + 3
Simplifying further:
-j = 3
Now, we can multiply both sides of the equation by -1 to solve for j:
(-1)(-j) = (-1)(3)
This simplifies to:
j = -3
So, one solution to the equation j = 2j + 3 is j = -3.
To find a second solution, we can substitute j = -3 back into the original equation:
-3 = 2(-3) + 3
Simplifying:
-3 = -6 + 3
-3 = -3
Since -3 is equal to -3, it is a valid solution.
Therefore, the equation j = 2j + 3 has two solutions: j = -3 and j = -3.