How do you answer this equation?

Question

12x+(-4)+42=17x+8

Answer 1

12x + (-4) + 42 = 17x + 8

 

Well since addition can happen in any order, let's start with the easy part:

(-4) + 42  is the same as  42 - 4  which is  38

 

12x + 38 = 17x + 8

 

Well if something plus 38 is the same as another thing plus 8, the second thing is 30 bigger. (i.e. Subtract 8 from both sides.)

 

12x + 30 = 17x

 

Now, if 12 x's plus 30 is the same as 17 x's, 30 must be 5 x's. (i.e. Subtract 12x from both sides)

 

30 = 5x

 

Finally if 5 x's is 30, take 30, divide it into 5 equal parts, and one of those parts is a single x. In this case, 30 divided by 5 is 6, are value of x. (i.e. divide by 5 on both sides.)

 

6 = x

 

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12x + (-4) + 42 = 17x + 8

 

We can then check that we got the right answer by replacing (substituting) x with 6 in the original problem.

 

12(6) + (-4) + 42 = 17(6) + 8

 

Multiply 12 and 17 by 6 to get 72 and 102 (respectively).

 

72 + (-4) + 42 = 102 + 8

 

Add up both sides separately to get:

 

110 = 110

 

Both sides are equal (110) when x = 6, so we had the right value for x!