Question

How do you solve $ \dfrac{7}{3}\left( {x + \dfrac{9}{{28}}} \right) = 20 $ ?

Answer 1

Hint: In order to determine the value of variable $ x $ in the above equation, first multiply both sides with the number $ \dfrac{3}{7} $ and simplify the equation. Now use the rules of transposing terms to transpose terms having $ (x) $ on the Left-hand side and constant value terms on the Right-Hand side of the equation. Combine and solve like terms get your desired solution.

Complete step-by-step answer:
 We are given a linear equation in one variable $ \dfrac{7}{3}\left( {x + \dfrac{9}{{28}}} \right) = 20 $ .and we have to solve this equation for variable ( $ x $ ).
 $ \Rightarrow \dfrac{7}{3}\left( {x + \dfrac{9}{{28}}} \right) = 20 $
Multiplying both sides of the equation with the number $ \dfrac{3}{7} $ , we get
 $
   \Rightarrow \dfrac{3}{7} \times \dfrac{7}{3}\left( {x + \dfrac{9}{{28}}} \right) = \dfrac{3}{7} \times 20 \\
   \Rightarrow x + \dfrac{9}{{28}} = \dfrac{{60}}{7} \;
  $
Now combining like terms on both of the sides. Terms having $ x $ will on the Left-Hand side of the equation and constant terms on the right-hand side.
Let’s recall one basic property of transposing terms that on transposing any term from one side to another the sign of that term get reversed .In our case, $ \dfrac{9}{{28}} $ in left-hand side will become $ - \dfrac{9}{{28}} $ on right hand side .
After transposing terms our equation becomes
 $ \Rightarrow x = \dfrac{{60}}{7} - \dfrac{9}{{28}} $
Taking LCM of both terms and simplifying further we get
 $
   \Rightarrow x = \dfrac{{\left( 4 \right)60 - 9}}{{28}} \\
   \Rightarrow x = \dfrac{{240 - 9}}{{28}} \\
   \Rightarrow x = \dfrac{{231}}{{28}} \;
  $
Therefore, the solution to the equation $ \dfrac{7}{3}\left( {x + \dfrac{9}{{28}}} \right) = 20 $ is equal to $ x = \dfrac{{231}}{{28}} $ .
So, the correct answer is “ $ x = \dfrac{{231}}{{28}} $ ”.

Note: Linear Equation: A linear equation is a equation which can be represented in the form of $ ax + c $ where $ x $ is the unknown variable and a,c are the numbers known where $ a \ne 0 $ .If $ a = 0 $ then the equation will become constant value and will no more be a linear equation .
The degree of the variable in the linear equation is of the order 1.
Every Linear equation has 1 root.