What’s the solution of 12(x+1)=36
First, we need to distribute the 12 to BOTH terms in the parentheses. This means that we multiple both the x and the 1 by 12.
12(x+1)=36
12x + 12 = 36
From here, we need to do opposite operations in order to get x alone. The opposite of adding 12 is subtracting 12. We will subtract 12 from 12 so that it "cancels," but whatever we do to one side of the equation, we must also do to the other side of the equation, so that we keep the equation balanced.
12x + 12 = 36
-12 -12
12x = 24
When a number is "attached" to a variable, it indicates multiplication. The 12 is multiply our x. The opposite of multiplying by 12 is dividing by 12, and so we divide by 12 on both sides of the equation to get x alone.
12x = 24
12 12
x=2 is our answer.
We can also check that x=2 is the correct answer by plugging it back in to our original equation:
12(x+1)=36 replace x with 2
12(2+1)=36 solve using order of operations (or distribute property)
12(3)=36 solve
36 = 36 YES
Since when we plugged in our answer x=2 into our original equation, but sides came out to be the same number, our answer is in fact x=2
Note: Students often forget to distribute the number outside (in this case, 12), to both terms inside the parentheses, so I like to draw an arrow connecting the 12 to the x, and another arrow connecting the 12 to the 1, almost as if the 12 is "high fiving" each term. I not only show my students how to solve math problems, but am very good at anticipating their mistakes, and providing strategies to help students avoid these pitfalls.
