Question

How do you solve \[\dfrac{1}{2}x - \dfrac{5}{3} = - \dfrac{1}{2}x + \dfrac{{19}}{4}\]?

Answer 1

Hint: First of all we will move all constants on the right hand side of the equation and the term with variable on the left hand side of the equation and then simplify for the resultant required value for “x”.

Complete step by step solution:
Take the given expression: \[\dfrac{1}{2}x - \dfrac{5}{3} = - \dfrac{1}{2}x + \dfrac{{19}}{4}\]
Move the constant from the left hand side of the equation to the right hand side of the equation and the term with the variable from right hand side to the left hand side. When you move any term from one side to another then the sign of the term also changes. Positive term becomes negative term and vice versa.
\[\dfrac{1}{2}x + \dfrac{1}{2}x = + \dfrac{{19}}{4} + \dfrac{5}{3}\]
Simplify the above expression, combine the numerators since the denominators are the same. Also, simplify the right hand side of the equation finding the LCM (Least common Multiple)
\[\dfrac{{1x + 1x}}{2} = \dfrac{{19(3) + 5(4)}}{{4(3)}}\]
Simplify the above expression taking the product of the terms on the numerator.
\[\dfrac{{2x}}{2} = \dfrac{{57 + 20}}{{12}}\]
Common factors from the numerator and the denominator cancels each other on the left hand side of the equation. Also, find the addition of terms on the numerator on the right.
 $ \Rightarrow x = \dfrac{{77}}{{12}} $
This is the required solution.
So, the correct answer is “ $ x = \dfrac{{77}}{{12}} $ ”.

Note: Be careful about the sign convention while moving any term from one side to another the sign of the term also changes. Positive term becomes negative term and the negative term becomes positive term. Always remember that to combine the numerators, you should have the common denominators and for that LCM (least common multiple) should be taken first for further simplification.