Question

Solve for x: \[0.2\left( {2x - 1} \right) - 0.5\left( {3x - 1} \right) = 0.4\]
a). \[ - \dfrac{1}{{11}}\]
b). \[ - \dfrac{1}{{14}}\]
c). \[ - \dfrac{1}{{17}}\]
d). \[ - \dfrac{1}{{19}}\]

Answer 1

Hint: Here we have a linear equation with a variable ‘x’. Here we need to solve for ‘x’. We can solve this using the transposition method. That is we group the ‘p’ terms on one side and constants on the other side of the equation. It will be difficult to solve decimal values, so first we multiply the whole equation by 10, then we solve it.

Complete step-by-step solution:
Given, \[0.2\left( {2x - 1} \right) - 0.5\left( {3x - 1} \right) = 0.4\].
Multiply the whole equation by 10, we have
 \[2\left( {2x - 1} \right) - 5\left( {3x - 1} \right) = 4\]
Now expanding the brackets we have
\[4x - 2 - 15x + 5 = 4\]
Simplifying we have
\[ - 11x + 3 = 4\]
We transpose \[3\] which is present in the left-hand side of the equation to the right-hand side of the equation by subtracting \[3\]on the right-hand side of the equation.
\[ - 11x = 4 - 3\]
\[\Rightarrow - 11x = 1\]
Now divide the whole equation by $-11$
\[ \Rightarrow x = - \dfrac{1}{{11}}\].
Hence the required option is (a).

Note: By simplifying we have obtained the answer for ‘p’. We can check whether the obtained value of ‘p’ is correct or not. To check we simply substitute the obtained value of ‘p’ in the given problem. If L.H.S is equal to R.H.S. then our 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.