Question

How do you solve \[ - \dfrac{3}{4}x = 12\]?

Answer 1

Hint:In the given problem we need to solve this for ‘x’. We can solve this using the
transposition method. The common transposition method is to do the same thing (mathematically)
to both sides of the equation, with the aim of bringing like terms together and isolating the variable
(or the unknown quantity).

Complete step by step solution:
Given, \[ - \dfrac{3}{4}x = 12\]
We have ‘x’ in the left hand side of the equation.

We have 4 on the left hand side of the equation. We transpose ‘4’ to the right side of the equation
by multiplying 4 on both sides.
\[ \Rightarrow 4 \times - \dfrac{3}{4}x = 12 \times 4\]
\[ \Rightarrow - 3x = 12 \times 4\].

Since we have 3 on the left hand side. We transpose 3 by dividing the whole equation by ‘3’.
\[ \Rightarrow - \dfrac{{3x}}{3} = \dfrac{{12 \times 4}}{3}\]
\[ \Rightarrow - x = \dfrac{{12 \times 4}}{3}\]

Multiplying negative sign on both sides of the equation
\[ \Rightarrow x = - \dfrac{{12 \times 4}}{3}\]
\[ \Rightarrow x = - 4 \times 4\]
\[ \Rightarrow x = - 16\].

Thus we have x = -16

Note: We can check if the obtained answer is correct or not. If we substitute \[x = - 16\] in the above equation we will have \[12 = 12\]. Hence our obtained answer is correct. If we want to transpose the addition number to any side of the equation we subtract it with the same number on both sides of the equation. Similarly if we want to transpose the negative number to any side of the equation we add with the same number on both sides of the equation. Similarly if we have multiplication we use division to transpose. If we have division we use multiplication to transpose. Follow the same procedure for these kinds of problems.