Question

How do you solve \[\dfrac{{m + 1}}{4} = \dfrac{{3m + 6}}{7}\] ?

Answer 1

Hint:To solve this equation find out the value of m by cross multiplying the terms given, by this we can get the value of m.

Complete step by step answer:
As the given equation is linear equation to solve this let us write the given equation as
\[\dfrac{{m + 1}}{4} = \dfrac{{3m + 6}}{7}\]
To solve this cross multiply the equation i.e.,
\[7\left( {m + 1} \right)\]= \[4\left( {3m + 6} \right)\]
After multiplying the terms, we get
\[7m + 7 = 12m + 24\]
\[12m - 7m = 7 - 24\]
On further simplification
\[5m = - 17\]
Therefore, the value of m is
\[m = - \dfrac{{17}}{5}\]
Additional information: Linear equations are equations of the first order. These equations are defined for lines in the coordinate system. An equation for a straight line is called a linear equation.
The general representation of the straight-line equation is \[y = mx + b\], where m is the slope of the line and b is the y-intercept.
To solve Linear Equations having 2 variables, there are different methods. Following are some of them:
1. Method of substitution
2. Cross multiplication method
3. Method of elimination
4. Determinant methods
Linear equations are those equations that are of the first order. These equations are defined for lines in the coordinate system. Linear equations are also first-degree equations as it has the highest exponent of variables as 1.

Note: Equations with linear expressions in one variable only are known as linear equations in one variable. An algebraic equation is an equality involving variables. Here to find the value of m, simplify both the equations of LHS and RHS i.e., the expression on the left of the equality sign is the Left- Hand Side (LHS). The expression on the right of the equality sign is the Right-Hand Side (RHS). In an equation the values of the expressions on the LHS and RHS are equal.