Answer:
j = 1.5
Step-by-step explanation:
You want to solve the equation 0.3j-(0.1j-3) + 0.1 = 2 (j+0.1) + 0.2 for the value of j.
It usually works well to simplify such an equation as the first step. That means eliminating parentheses and combining like terms.
0.3j-(0.1j-3) + 0.1 = 2 (j+0.1) + 0.2 . . . . . . given
0.3j -0.1j +3 +0.1 = 2j +0.2 +0.2 . . . . . . eliminate parentheses
0.2j +3.1 = 2j +0.4 . . . . . . . . . . . . collect terms
2.7 = 1.8j . . . . . . . . . . . subtract (0.2j +0.4)
1.5 = j . . . . . . . . . divide by 1.8
The solution is j = 1.5.
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Additional comment
You are often taught to solve this kind of 3-step equation by subtracting the unwanted variable term and the unwanted constant term in two steps. (The third step is dividing by the coefficient of the variable.) Here, we show those subtractions being done both at once.
The variable term we choose to subtract is the one with the smallest coefficient. That way, the result of the subtraction (1.8j) leaves the coefficient of the variable as a positive number.
Sometimes the variable term on the right is subtracted, so you end up with a "j = " equation. In that case, the equation you would be solving as the last step is ...
-1.8j = -2.7
which requires arithmetic with negative numbers. Negative numbers tend to be associated with more mistakes, so we choose not to go there.
