Question

Solve the following equation: $ 7m+\dfrac{19}{2}=13 $ ?
(a) $ \dfrac{1}{2} $
(b) 1
(c) $ \dfrac{-1}{2} $
(d) -1

Answer 1

Hint:
 We start solving the problem by subtracting the given equation with $ \dfrac{19}{2} $ on both sides. We then make the necessary calculations and then divide both sides of the obtained equation with 7. We then make the necessary calculations to get the required value of ‘m’.

Complete step by step answer:
According to the problem, we are asked to solve the given equation $ 7m+\dfrac{19}{2}=13 $ .
So, we have the given equation $ 7m+\dfrac{19}{2}=13 $ ---(1).
Let us subtract with $ \dfrac{19}{2} $ on both sides of the equation (1).
 $ \Rightarrow 7m+\dfrac{19}{2}-\dfrac{19}{2}=13-\dfrac{19}{2} $ .
 $ \Rightarrow 7m=\dfrac{26-19}{2} $ .
 $ \Rightarrow 7m=\dfrac{7}{2} $ ---(2).
Let us divide with 7 into both sides of the equation (2).
 $ \Rightarrow \dfrac{7m}{7}=\dfrac{\dfrac{7}{2}}{7} $ .
 $ \Rightarrow m=\dfrac{1}{2} $ .
So, we have found the value of ‘m’ as $ \dfrac{1}{2} $ .
∴ The value of ‘m’ is $ \dfrac{1}{2} $ .
The correct option for the given problem is (a).

Note:
 We can also solve this problem by applying the trial and error method for the values of ‘m’ to get the required answer. We should not make calculation mistakes while making addition or subtraction involving the fractions. We can also find the value of squares or cubes of the obtained value of the ‘m’. We can also expect problems to find the value of ‘y’ if it is defined as $ y=4m $. Similarly, we can expect problems to find the general equation of all the lines with the slope of those lines as ‘m’.