Question

How do you solve $\dfrac{{\left| { - 4 - 3n} \right|}}{4} = 2?$

Answer 1

Hint: As we know that the above given equation is a linear equation. An equation for a straight line is called a linear equation. The standard form of linear equations in two variables is $Ax + By = C$ . When an equation is given in this form it’s also pretty easy to find both intercepts $(x,y)$ . By transferring all the numerical terms to the right hand side value gives the required solution.

Complete step by step solution:
As we know that the above given equation is a linear equation and to solve for $n$ we need to isolate the term containing $n$ on the left hand side i.e. to simplify $\dfrac{{\left| { - 4 - 3n} \right|}}{4} = 2.$
Here we will transfer the $4$to the right hand side and we get $\left| { - 4 - 3n} \right| = 2 \times 4$.
It gives us the value $\left| { - 4 - 3n} \right| = 8$. Now we will use the formula $f\left| n \right| = a$, then we can write it as $f(n) = - a$ or $f(n) = a.$
By applying the above formula we have, $( - 4 - 3n) = 8$ or $( - 4 - 3n) = - 8$.
Solving the first condition: $ - 4 - 3n = 8 \Rightarrow - 3n = 8 + 4$. Therefore it gives us the value of $n = \dfrac{{ - 12}}{3} = - 4$.
Now we solve the second condition i.e. $ - 4 - 3n = - 8 \Rightarrow - 3n = - 8 + 4$.
On further solving it gives us the value $ - 3n = - 4 \Rightarrow n = \dfrac{4}{3}$.

Hence the required value of $n$ is $ - 4$ or $\dfrac{4}{3}.$

Note: We should keep in mind the positive and negative signs while calculating the value of any variable as it will change it’s slope and value. In the equation $Ax + By = C$ ,$A$ and $B$are real numbers and $C$ is a constant, it can be equal to zero$(0)$ also. These types of equations are of first order. 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 $y = mx + c$ ,where $m$ is the slope of the line and $b$ in the equation is the y-intercept and $x$ and $y$are the coordinates of x-axis and y-axis , respectively.