Question

How do you solve for $ x $ in $ 5x + 7x = 72 $ ?

Answer 1

Hint: Every equation is required to be simplified and which can easily be done by using one of the laws of arithmetic that is, the distributive law. This law states that multiplying a number by a group of numbers added together is the same as doing each multiplication separately. In mathematical terms, $ a(b + c) = ab + ac $ . Here, in this question first we are required to simplify the equation and then further solve it to get the value of $ x $ .

Complete step-by-step answer:
Firstly, we need to simplify the given equation which can easily be done by using distributive law of arithmetic. Using this law, we get,
$\Rightarrow 5 \times x + 7 \times x = \left( {5 + 7} \right)x $
Since we know that $ 5 + 7 = 12 $ so, we can rewrite our equation as
$\Rightarrow 12x = 72 $
Now we are required to do a transformation of this equation which can be done by using another law that states that if two numeric values are equal, you can divide both of them by the same number which should not be equal to zero, and the results will be equal. So, we divide the entire equation by $ 12 $ so that we can get $ x $ alone, without any numeric value on the left-hand side.
 $\Rightarrow \dfrac{{12x}}{{12}} = \dfrac{{72}}{{12}} $
 $ x = 6 $
Hence, the value of $ x $ is $ 6 $ .
So, the correct answer is “x=6”.

Note: Now that we know the value of $ x $ is $ 6 $ , there is a way to double check our answer. In order to double check the solution we are supposed to substitute the value of $ x $ which we got as $ 6 $ in the given equation, $ 5x + 7x = 72 $
 $
  5x + 7x = 72 \\
  5(6) + 7(6) = 72 \\
  30 + 42 = 72 \\
  72 = 72 \;
  $
Now, the left-hand side is equal to the right-hand side. So, we can conclude that our solution or the value of $ x $ which we calculated was correct.