"The sum of 6 times a number and 3 is 2"
We can break this down as "the sum of _____ and _____ is 2" or ______ + ______ = 2
In the statement our blanks are "6 times a number" and "3", so we can fill in our second blank:
_____ + 3 = 2
When we see "a number" we should use a variable to represent that number, let's call it x. Then "6 times a number" can be represented by 6x, and we can fill in our other blank:
6x+3=2
Now we perform a little manipulation, first by subtracting 3 from each side:
(6x + 3) - 3 = (2 - 3) --> 6x + (3 - 3) = (2 - 3) --> 6x + 0 = -1 --> 6x = -1
and then divide both sides by 6:
(6x) / 6 = -1 / 6 --> (6/6)x = -1/6 --> (1)x = -1 / 6 --> x = -1/6
and we arrive at x = -1/6, so our number is -1/6, for which we can verify:
6(-1 / 6) + 3 = -1 + 3 = 3 - 1 = 2
