Question

How do you solve the equation \[\dfrac{{3x - 8}}{x} = 2\]?

Answer 1

Hint: In the given problem we need to solve this for ‘x’. We can solve this using the transposition method. That is we group the ‘x’ terms on one side and constants on the other side of the equation. To separate the ‘x’ term we cross multiply and simplify it.

Complete step-by-step solution:
Given, \[\dfrac{{3x - 8}}{x} = 2\].
Now cross multiplying we have,
\[3x - 8 = 2x\]
We transpose \[2x\] which is present in the right-hand side of the equation to the left-hand side of the equation by subtracting \[2x\] on the left-hand side of the equation.
\[3x - 8 - 2x = 0\]
Now similarly we transpose the constant term to the right-hand side of the equation.
\[3x - 2x = 8\]
We can see that the variable ‘x’ and the constants are separated, then
\[x = 8\]
\[ \Rightarrow x = 8\]

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.
\[\dfrac{{3(8) - 8}}{{(8)}} = 2\]
\[\dfrac{{24 - 8}}{8} = 2\]
\[\dfrac{{16}}{8} = 2\]
\[ \Rightarrow 2 = 2\]
Hence the obtained answer is correct.
In the above, we did the transpose of addition and subtraction. 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.