Question

How do you solve $4 + 2x = 36$ ?

Answer 1

Hint: In this question, we are given an algebraic expression containing an unknown variable quantity “x” linked to the constant numerical values via arithmetic operations like addition, subtraction, multiplication and division. We know that for finding the values of “n” unknown variable quantities, we need “n” number of equations. In this question, we have exactly one equation to find the value of one unknown quantity, so its value can be obtained easily. After simplifying the equation, we will rearrange the equation such that all the terms containing “x” are on one side and the constant terms are present on the other side. Then we will find the value of x by applying the given arithmetic operations.

Complete step-by-step solution:
We are given that $4 + 2x = 36$
On applying the distributive property on the left-hand side, we get –
$\Rightarrow 2(2 + x) = 36$
We will take 2 to the right-hand side –
$\Rightarrow 2 + x = \dfrac{{36}}{2}$
We will simplify the obtained fraction by canceling out the common factors –
$\Rightarrow 2 + x = 18$
Now, we will take 2 to the right-hand side so that one side contains only x and the other side contains constant values –
$
  \Rightarrow x = 18 - 2 \\
   \Rightarrow x = 16 \\
 $
Hence, when $4 + 2x = 36$ , we get $x = 16$ .

Note: We have simplified the equation by using the distributive property. According to the distributive property, the product of a number with the sum of two other numbers is equal to the product of that number with the first number plus the product of that number with the second number and vice-versa, that is, $a(b + c) = ab + ac\,or\,ab + ac = a(b + c)$ , so we have taken 2 common from the left-hand side and then take it to the right-hand side. We can also solve the equation by simply taking 4 to the right-hand side and then dividing both the sides by 2.