Question

Find \[n\] if \[7n + 5 = 19\].

Answer 1

Hint:
Here we will take the constant term on the left side of the given linear equation to the right side of the equal sign. Then we will divide the whole equation by 7. We will solve the equation further to get our desired answer.

Complete step by step solution:
The equation given to us is:
\[7n + 5 = 19\]
We can see that it is a Linear equation with one unknown variable \[n\].
Next, we have to find the value of \[n\] so we will solve the above equation as,
\[7n + 5 = 19\]
Subtracting 5 on both the sides, we get
\[\begin{array}{l} \Rightarrow 7n = 19 - 5\\ \Rightarrow 7n = 14\end{array}\]
Now we will divide the whole equation by 7 and get,
\[\dfrac{{7n}}{7} = \dfrac{{14}}{7}\]
\[ \Rightarrow n = 2\]

Therefore, we get the value of \[n = 2\].

Additional Information:
In order to solve for a variable, the number of unknown variables should be equal to the number of equations then only we can find the value of all the variables. If the number of equations is more than one and we have to find the value of one variable, then that value of the variable should satisfy all the equations in order to be correct. If two equations and two unknown variables are given then we solve the equation by substituting and eliminating methods to get our answer.

Note:
An equation is said to be linear if the power of the variable is one and we don’t have any other variable with a power of more than one. A linear equation has only one solution because the highest degree of the equation is only 1. The number of solutions of a particular equation depends on its highest degree of variables. For example, a quadratic equation has the highest degree of 2 and so it has two solutions.