Question

How do you solve $ \dfrac{k}{7}+3-2k=-3 $ ?

Answer 1

Hint: We solve the given linear equation by simplifying the equation $ \dfrac{k}{7}+3-2k=-3 $ . Then we multiply the equation with 7 to remove the fraction. We then divide both sides of the equation with 13. We use the G.C.D of the denominator and the numerator to divide both of them. We get the simplified form as the G.C.D is 1.

Complete step-by-step answer:
The given equation $ \dfrac{k}{7}+3-2k=-3 $ is a linear equation of $ k $ .
We first try to simplify it by taking the constants and the variables separately on the opposite sides of the equality.
 $
 \dfrac{k}{7}+3-2k=-3 \\
  \Rightarrow \dfrac{k}{7}-2k=-3-3=-6 \\
 $
We multiply 7 both sides.
 $
 -7\left( \dfrac{k}{7}-2k \right)=\left( -6 \right)\times \left( -7 \right) \\
 \Rightarrow 14k-k=42 \\
  \Rightarrow 13k=42 \\
 $
We divide both sides of the equation $ 13k=42 $ with 13.
\[
 \dfrac{13k}{13}=\dfrac{42}{13} \\
  \Rightarrow k=\dfrac{42}{13} \\
\]
We need to find the simplified form of the proper fraction $ \dfrac{42}{13} $ .
Simplified form is achieved when the G.C.D of the denominator and the numerator is 1.
For any fraction $ \dfrac{p}{q} $ , we first find the G.C.D of the denominator and the numerator. If it’s 1 then it’s already in its simplified form and if the G.C.D of the denominator and the numerator is any other number d then we need to divide the denominator and the numerator with d and get the simplified fraction form as $ \dfrac{{}^{p}/{}_{d}}{{}^{q}/{}_{d}} $ .
For our given fraction $ \dfrac{42}{13} $ , the G.C.D of the denominator and the numerator is 1.
Therefore, this is the most simplified form of the fraction.
Therefore, the solution of $ \dfrac{k}{7}+3-2k=-3 $ is $ \dfrac{42}{13} $ .
So, the correct answer is “ $ \dfrac{42}{13} $ ”.

Note: The process of simplification comes from the G.C.D of the denominator and the numerator. In case of a linear equation, the number of solutions in every case will be 1. The simplified form will be equal to the value of $ k $ .