Question

What is the value of k in the equation 3/2(k+2/5)=2 1/3 ?

Answer 1

Let us first write down the given equation and then start simplifying.
3/2(k + 2/5) = 2 1/3
3/(2k + 4/5) = 7/3
3/[(10k + 4)/5] = 7/3
3 * 3 = 7[(10k +4)/5]
9 = (70k + 28)/5
9 * 5 = 70k + 28
45 = 70k + 28
45 - 28 = 70k
17= 70k
Reversing both sides we get
70k = 17
k = 17/70
So the value of k comes out to be 17/70 and it is impossible to simplify it further.

Answer 2

$\dfrac{3}{2}\left(k+\dfrac{2}{5}\right)=2\dfrac{1}{3}\\ \dfrac{3}{2}\left(k+\dfrac{2}{5}\right)=\dfrac{7}{3}\\\ k+\dfrac{2}{5}=\dfrac{7}{3}\cdot\dfrac{2}{3}\\ k+\dfrac{2}{5}=\dfrac{14}{9}\\ k=\dfrac{14}{9}-\dfrac{2}{5}\\ k=\dfrac{70}{45}-\dfrac{18}{45}\\ k=\dfrac{52}{45}$