Explanation:
To solve any equation that is linear in the variable of interest, you first look at what is done to the variable, using the Order of Operations as your guide.
Here, the variable is ...
- multiplied by "a"
- the product has "b" added to it.
You find the value of the variable by reversing these steps, starting from the last one on the list and working up the list.
To "undo" the addition of "b", we add its opposite (-b) to the equation. The rules of equality tell you that anything you do to one side of the equation must also be done to the other side, so we add -b to both sides:
ax +b -b = c -b
ax = c -b . . . . . . . . simplify
To "undo" the multiplication by "a", we multiply by its reciprocal. That is, we multiply by 1/a, or, equivalently, divide by "a". Again, we must do this to both sides of the equation:
(1/a)ax = (1/a)(c -b)
x = (c -b)/a . . . . . . . simplify
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In short, we subtract the added constant (b) and divide by the multiplier (a).
