Question

Solve
\[\dfrac{x}{2} + \dfrac{3}{2} = \dfrac{{2x}}{5} - 1\]

Answer 1

Hint: Here we need to solve for ‘x’. We simplify the left-hand side and the right-hand side of the equation by the help of LCM. Then we cross multiply it. After that, we separate the variable that is ‘x’ on one side of the equation and constants on the other side of the equation. Then applying the suitable mathematical operation we will have the required answer.

Complete step-by-step answer:
Given, \[\dfrac{x}{2} + \dfrac{3}{2} = \dfrac{{2x}}{5} - 1\].
Now take LCM on LHS, and simplifying we have,
\[\dfrac{{x + 3}}{2} = \dfrac{{2x}}{5} - 1\]
Similarly, we take LCM on RHS,
\[\dfrac{{x + 3}}{2} = \dfrac{{2x - 5}}{5}\].
Now cross multiplying we have,
\[5\left( {x + 3} \right) = 2\left( {2x - 5} \right)\]
Now expanding the brackets we have,
\[5x + 15 = 4x - 10\]
Now shift 15 to the RHS of the equation,
\[5x = 4x - 10 - 15\]
Now shifting or transposing 4x to the LHS,
\[5x - 4x = - 10 - 15\]
Thus we have separated constants and variables,
\[ \Rightarrow x = - 25\]. This is the required answer.

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.
\[\dfrac{{ - 25}}{2} + \dfrac{3}{2} = \dfrac{{2\left( { - 25} \right)}}{5} - 1\]
\[\dfrac{{ - 25 + 3}}{2} = \dfrac{{ - 50}}{5} - 1\]
\[\dfrac{{ - 22}}{2} = - 10 - 1\]
Simplifying we have,
\[ \Rightarrow - 11 = - 11\].
That is LHS=RHS. Hence the obtained is correct.
While shifting the terms from one side of the equation to the other side the sign will change. That is if we want to transpose a positive number to the other side of the equation the sign will change to negative.