Question

Solve the equation:
 $ \dfrac{{15}}{4} - 7x = 9 $

Answer 1

Hint: The equations which are solved by more than one basic operation can be called the multi-step equation. The equation given:
 $ \dfrac{{15}}{4} - 7x = 9 $ is also a multi-step equation. The operations that we use to solve the equation can be addition, subtraction, multiplication, division, squaring or taking root of the equation. The operations must be done on both sides of the equation to maintain equality.

Complete step-by-step answer:
The given equation
 $ \dfrac{{15}}{4} - 7x = 9 $
Is a multi-step equation and will be solved by doing basic operations on both sides to separate the variable from the constant.
First we will subtract $ \dfrac{{15}}{4} $ from both the sides of the equation, so that the constant on the left hand side of the equation can be removed. So we can write,
 $ \Rightarrow \dfrac{{15}}{4} - 7x - \dfrac{{15}}{4} = 9 - \dfrac{{15}}{4} $
The subtraction of fraction and the number on the right side of the equation will then be solved as below,
 $ \Rightarrow - 7x = \dfrac{{36 - 15}}{4} $
 $ \Rightarrow - 7x = \dfrac{{21}}{4} $
Now we will divide both sides of the equation by $ 7 $ in order to remove the coefficient present in the variable.
 $ \Rightarrow \dfrac{{ - 7x}}{7} = \dfrac{{21}}{{4 \times 7}} $ $ $
We get
 $ \Rightarrow - x = \dfrac{3}{4} $
Multiply both sides by $ - 1 $ to remove negative sign from the variable we get,
 $ \begin{gathered}
   \Rightarrow - x \times - 1 = \dfrac{3}{4} \times - 1 \\
   \Rightarrow x = - \dfrac{3}{4} \\
\end{gathered} $
Thus the value of the variable $ x $ is
 $ x = \dfrac{{ - 3}}{4} $ or $ x = - 0.75 $
So, the correct answer is “ $ x = \dfrac{{ - 3}}{4} $ or $ x = - 0.75 $ ”.

Note: Alternate method: This question could also have been solved by the method of rearrangement of constants in an equation. We would have proceeded as below, remembering that sign of the constant changes when it changes its side i.e. a negative integer will become a positive integer on moving to the other side of the equation.
 $ \Rightarrow \dfrac{{15}}{4} - 7x = 9 $
 $ \Rightarrow \dfrac{{15}}{4} - 9 = 7x $
 $ \Rightarrow \dfrac{{15 - 36}}{4} = 7x $
 $ \Rightarrow \dfrac{{ - 21}}{4} = 7x $
 $ $ solving by putting $ 7 $ to the denominator and dividing we get,
 $ \Rightarrow x = \dfrac{{ - 3}}{4} $ or $ x = - 0.75 $