Question

How do you solve $\dfrac{3}{4}n + 16 = 2 - \dfrac{1}{8}n$ ?

Answer 1

Hint: We can solve this question by separating all the terms containing variables to the one side of the equation that is on the left hand side and all the constant values to the other side of the equation.

Complete step by step answer:
We will start by writing the main equation:
$ \Rightarrow \dfrac{3}{4}n + 16 = 2 - \dfrac{1}{8}n$
Move all the terms containing n to the left side of the equation:
$ \Rightarrow \dfrac{3}{4}n + \dfrac{1}{8}n = 2 - 16$
Simplify:
$ \Rightarrow \dfrac{{3n}}{4} + \dfrac{n}{8} = - 14$
To write $\dfrac{{3n}}{4}$as a fraction with a common denominator, multiply it with $\dfrac{2}{2}$
$ \Rightarrow \dfrac{{3n}}{4} \times \dfrac{2}{2} + \dfrac{n}{8} = - 14$
$ \Rightarrow \dfrac{{6n}}{8} + \dfrac{n}{8} = - 14$
Combine the numerator over the common denominator:
$ \Rightarrow \dfrac{{6n + n}}{8} = - 14$
Simplify the numerator:
$ \Rightarrow \dfrac{{7n}}{8} = - 14$
Multiply both side of the equation by $\dfrac{8}{7}$
$ \Rightarrow \dfrac{{7n}}{8} \times \dfrac{8}{7} = - 14 \times \dfrac{8}{7}$
Simplify both the sides of the equation:
Cancel the common factor of 8:
$ \Rightarrow \dfrac{{7n}}{{\not{8}}} \times \dfrac{{\not{8}}}{7} = - 14 \times \dfrac{8}{7}$
Rewrite the expression:
$ \Rightarrow \dfrac{{7n}}{7} = - 14 \times \dfrac{8}{7}$
Cancel the common factor of 7:
$ \Rightarrow \dfrac{{\not{7}n}}{{\not{7}}} = - 14 \times \dfrac{8}{7}$
Rewrite the expression:
$ \Rightarrow n = - 14 \times \dfrac{8}{7}$
Simplify by factor 7 out of -14:
$ \Rightarrow n = - 2 \times 7 \times \dfrac{8}{7}$
Cancel the common factor of 7:
$ \Rightarrow n = - 2 \times \not{7} \times \dfrac{8}{{\not{7}}}$
Rewrite the expression:
$ \Rightarrow n = - 2 \times 8$
Simplify:
$ \Rightarrow n = - 16$

Hence, $n = - 16$ is the final solution.

Note: After finding the value of the variable n we can check for the solution if it is correct or not by substituting the value of the variable to the equation given in the question.
If the left hand side of the equation comes out to be equal to the right hand side of the equation that means we have solved the equation correctly.
You can check by substituting the value of variable n to both the sides of the equation:
$ \Rightarrow \dfrac{3}{4}n + 16 = 2 - \dfrac{1}{8}n$
Substituting the value of n to both the sides:
$ \Rightarrow \dfrac{3}{4} \times - 16 + 16 = 2 - \dfrac{1}{8} \times - 16$
Simplify by factor 4 out of -16 in LHS and factor 8 out of -16 in RHS:
$ \Rightarrow \dfrac{3}{4} \times 4 \times - 4 + 16 = 2 - \dfrac{1}{8} \times 8 \times - 2$
Cancel the common factor of 4 in LHS and 8 in RHS:
$ \Rightarrow \dfrac{3}{{\not{4}}} \times \not{4} \times - 4 + 16 = 2 - \dfrac{1}{{\not{8}}} \times \not{8} \times - 2$
Rewrite the expression:
$ \Rightarrow 3 \times - 4 + 16 = 2 - 1 \times - 2$
Simplify both the sides:
$ \Rightarrow - 12 + 16 = 2 + 2$
$ \Rightarrow 4 = 4$
So, we can see that LHS=RHS that means our solution is correct.