Question

Solve the equation \[\dfrac{{3x}}{5} = 15\] for the value of x.

Answer 1

Hint: Here we need to solve for ‘x’. We know that we can solve this using the transposition method. That is we separate the variable term ‘x’ and the constant terms. First, we transpose 5 to the RHS by multiplying 5 on both sides of the equation. And then we simplify for ‘x’.

Complete step-by-step solution:
Given, \[\dfrac{{3x}}{5} = 15\].
We transpose \[5\] which is present in the left-hand side of the equation to the right-hand side of the equation by multiplying \[5\] on the right-hand side of the equation.
\[3x = 15 \times 5\]
\[\Rightarrow 3x = 75\]
We transpose 3 to the right-hand side of the equation by dividing 3 on the RHS.
\[\Rightarrow x = \dfrac{{75}}{3}\]
\[ \Rightarrow x = 25\]. This is the required result.

Note: We can check whether the obtained solution is correct or wrong. All we need to do is substituting the value of ‘x’ in the given problem.
\[\dfrac{{3x}}{5} = 15\]
\[\Rightarrow \dfrac{{3 \times 25}}{5} = 15\]
\[\Rightarrow 3 \times 5 = 15\]
\[ \Rightarrow 15 = 15\]
Hence the obtained answer is correct.
To transpose if we have addition, we use subtraction and vice versa. 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.