Question

How do you solve $ \dfrac{7}{4} + \dfrac{1}{5}x - 32 = \dfrac{4}{5}x $ ?

Answer 1

Hint: We are given the linear equation with fractional number and variable $ x $ . First, we will bring the two terms with the variable $ x $ on the left hand side of the equation and the other constant terms on the right side of the equation. After that using LCM, we will solve the equation and reach our final answer.

Complete step-by-step answer:
We are given the linear equation $ \dfrac{7}{4} + \dfrac{1}{5}x - 32 = \dfrac{4}{5}x $ .
Now, let us bring the terms with variables on the left hand side and all the other constant terms on the left hand side of the equation.
Therefore we get
 $
  \dfrac{7}{4} + \dfrac{1}{5}x - 32 = \dfrac{4}{5}x \\
   \Rightarrow \dfrac{1}{5}x - \dfrac{4}{5}x = 32 - \dfrac{7}{4} \;
  $
In this equation, the denominators of both the terms on the left hand side are the same. Therefore, we can rewrite this equation as:
 $
   \Rightarrow \dfrac{{1 - 4}}{5}x = 32 - \dfrac{7}{4} \\
   \Rightarrow \dfrac{{ - 3x}}{5} = 32 - \dfrac{7}{4} \;
  $
Now, we will take the LCM for the whole equation which will be the LCM of 5 and 4 which is 20. Therefore, we can rewrite the equation as:
\[
   \Rightarrow \dfrac{{ - 3x \times 4}}{{20}} = \dfrac{{32 \times 20}}{{20}} - \dfrac{{7 \times 5}}{{20}} \\
   \Rightarrow - 12x = 640 - 35 \\
   \Rightarrow - 12x = 605 \\
   \Rightarrow x = - \dfrac{{605}}{{12}} \;
 \]
We can also convert it into decimal form by simple division.
 \[ \Rightarrow x = - \dfrac{{605}}{{12}} = - 50.41\]
So, the correct answer is “50.41”.

Note: Here, we have used the method to solve the linear equations with fractions. For this, we transform it into the equations without fraction. This method is called the clearing of fraction. We do this by multiplying every term of both sides of the equation by the LCM of denominators. Therefore, each denominator will then divide into its multiple and we will then have an equation without fractions. After that, we can simply solve it as the linear equation with one variable without any fractions involved.