Question

Solve: $\dfrac{1}{2}m - \dfrac{3}{4}m - m = 2.5$

Answer 1

Hint: We can see that the equation given in the above question is linear. AS we know that an equation for a straight line is called a linear equation. The standard form of linear equations which have two variables is as follows: $Ax + By = C$ . IN this question we will take the L.C.M of the denominators of the expression on the left-hand side of the equation and then we will simply do this.

Complete step by step answer:
According to the question it is given that that the above equation is a linear equation and we have to solve for $m$ we need to isolate the term containing $m$ on the left-hand side.
We can also write the above equation in a simplified form as:
$ \Rightarrow \dfrac{1}{2}m - \dfrac{3}{4}m - \dfrac{m}{1} = 2.5$
Now we will take the L.C.M of the denominators of the L.H.S and we have:
$ \Rightarrow \dfrac{{2m + 3m - 4m}}{4} = 2.5$
We can take the denominator to the right-hand side by multiplying it with the value i.e.
$ \Rightarrow 5m - 4m = 4 \times 2.5$
Now we have the value:
$ \Rightarrow m = 10$
Hence the required answer is $m = 10$ .

Note:
We should always keep in mind the positive and negative signs while calculating the value of any variable as it will change it’s slope and value. We know the standard form of equation i.e. $Ax + By = C$ , where $A$ and $B$ are real numbers and $C$ is a constant, it can be equal to zero$(0)$ also. These types of equations are called first-order equations. It should be noted that linear equations are also first-degree equations as it has the highest exponent of variables as $1$ . The slope-intercept form of a linear equation is of the form $y = mx + c$ ,where $m$ is the slope of the line and $b$ in the equation is the y-intercept. So the point $x$ and $y$ are the coordinates of x-axis and y-axis , respectively.