Question

How do you solve for x: $ \dfrac{7}{{12}}(x - 3) = \dfrac{1}{3}x + 4 $

Answer 1

Hint: In this equation, we are given an expression in which an equation is separated by the equal to sign. As the expression contains a combination of an alphabet and numerical values (the alphabet represents an unknown variable quantity). To find the value of x from the given equation we will simplify the equation by bringing all the terms containing x on one side and all the constant terms on the other side and then applying arithmetic operations like addition, subtraction, multiplication and division.

Complete step-by-step answer:
We are given $ \dfrac{7}{{12}}(x - 3) = \dfrac{1}{3}x + 4 $ , to solve this equation we eliminate the denominator as follows –
 $
  \dfrac{7}{{12}}(x - 3) = \dfrac{1}{3}x + 4 \\
   \Rightarrow \dfrac{7}{{12}}(x - 3) = \dfrac{{x + 12}}{3} \\
   \Rightarrow 7(x - 3) = \dfrac{{12}}{3}(x + 12) \\
   \Rightarrow 7x - 21 = 4(x + 12) \\
   \Rightarrow 7x - 12 = 4x + 48 \\
   \Rightarrow 7x - 4x = 48 + 12 \\
   \Rightarrow 3x = 60 \\
   \Rightarrow x = \dfrac{{60}}{3} \\
   \Rightarrow x = 20 \;
  $
Hence, when $ \dfrac{7}{{12}}(x - 3) = \dfrac{1}{3}x + 4 $ , we get $ x = 20 $ .
So, the correct answer is “ $ x = 20 $ ”.

Note: While simplifying the equation, we find the common denominator of the right-hand side and then we see the denominator of the left-hand side in multiplication with the equation of the right-hand side. Then we factorize the numerator and the denominator, 12 can be written as a product of 3 and 4, in the denominator we have 3, so 3 is the common factor and is thus canceled out. Now the equation obtained is not in fraction form and is a simple algebraic expression that is solved as shown. When we are given a term that is in multiplication with two or more terms in a bracket, we multiply that term with each term of the bracket one by one. Following the same steps as in this solution, we can solve similar questions.