Solveeit Logo
Login

Question

Question: How do you solve \(\dfrac{{\left| { - 4 - 3n} \right|}}{4} = 2?\)...

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

Explanation

Solution

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=CAx + By = C . When an equation is given in this form it’s also pretty easy to find both intercepts (x,y)(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 nn we need to isolate the term containing nn on the left hand side i.e. to simplify ∣−4−3n∣4=2.\dfrac{{\left| { - 4 - 3n} \right|}}{4} = 2.
Here we will transfer the 44to the right hand side and we get ∣−4−3n∣=2×4\left| { - 4 - 3n} \right| = 2 \times 4.
It gives us the value ∣−4−3n∣=8\left| { - 4 - 3n} \right| = 8. Now we will use the formula f∣n∣=af\left| n \right| = a, then we can write it as f(n)=−af(n) = - a or f(n)=a.f(n) = a.
By applying the above formula we have, (−4−3n)=8( - 4 - 3n) = 8 or (−4−3n)=−8( - 4 - 3n) = - 8.
Solving the first condition: −4−3n=8⇒−3n=8+4 - 4 - 3n = 8 \Rightarrow - 3n = 8 + 4. Therefore it gives us the value of n=−123=−4n = \dfrac{{ - 12}}{3} = - 4.
Now we solve the second condition i.e. −4−3n=−8⇒−3n=−8+4 - 4 - 3n = - 8 \Rightarrow - 3n = - 8 + 4.
On further solving it gives us the value −3n=−4⇒n=43 - 3n = - 4 \Rightarrow n = \dfrac{4}{3}.

Hence the required value of nn is −4 - 4 or 43.\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=CAx + By = C ,AA and BBare real numbers and CC is a constant, it can be equal to zero(0)(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 11 . The slope intercept form of a linear equation is y=mx+cy = mx + c ,where mm is the slope of the line and bb in the equation is the y-intercept and xx and yyare the coordinates of x-axis and y-axis , respectively.