Question

Solve $ \dfrac{{2m}}{3} + 8 = \dfrac{m}{2} - 1 $ for the value of m.

Answer 1

Hint: First of all take LCM (least common multiple) on both the sides of the equation and simplify using the cross multiplication and frame the simplified equation and then make the subject “m” to get its value.

Complete step-by-step answer:
Take the given expression: $ \dfrac{{2m}}{3} + 8 = \dfrac{m}{2} - 1 $
Simplify both the sides of the equation considering the fraction and its denominator.
 $ \dfrac{{2m}}{3} + \dfrac{{8(3)}}{3} = \dfrac{m}{2} - \dfrac{{1(2)}}{2} $
Simplify both the sides of the equation, when denominators are the same then the numerators are combined.
 $ \dfrac{{2m + 24}}{3} = \dfrac{{m - 2}}{2} $
Perform cross multiplication when the numerator of one side is multiplied with the denominator of the opposite side and vice-versa.
 $ 2(2m + 24) = 3(m - 2) $
Multiply the term outside the bracket with the terms inside the bracket. When there is a positive sign outside the bracket then there is no change in the sign of the terms inside the bracket.
 $ 4m + 48 = 3m - 6 $
Move the term with “m” on the left hand side of the equation and the constants on the left hand side of the equation. When you move any term from one side to another then the sign of the terms also changes. Positive term changes to negative and vice-versa.
 $ 4m - 3m = - 6 - 48 $
Simplify the above expression
 $ m = - 54 $
This is the required solution.
So, the correct answer is “ $ m = - 54 $ ”.

Note: Be careful about the sign convention while simplification and moving terms from one side to another. The sign of the term is also changed. Also, remember when you combine two negative terms then you have to add both the terms and give a negative sign to the resultant value.