Answer:
[tex] k = \dfrac{5}{3} [/tex]
Step-by-step explanation:
It is actually a one-step equation.
If you have a number multiplying a variable equaling another number, then you need to do only one operation to solve; you need to multiply both sides by the reciprocal of the number multiplying the variable.
Here we have
[tex] \dfrac{3}{2} = \dfrac{9}{10}k [/tex]
First, switch sides to have the variable, k, on the left side.
[tex] \dfrac{9}{10}k = \dfrac{3}{2} [/tex]
You have a variable, k, multiplied by a number, the fraction 9/10, equaling another number, 3/2. To solve for k, multiply both sides by the reciprocal of 9/10 which is 10/9.
[tex] \dfrac{10}{9} \times \dfrac{9}{10}k = \dfrac{10}{9} \times \dfrac{3}{2} [/tex]
On the left side, you have the product of two reciprocals, 10/9 and 9/10, which equals 1, leaving just k.
On the right side, you must multiply the fraction 10/9 by 3/2 and then reduce.
[tex] k = \dfrac{30}{18} [/tex]
[tex] k = \dfrac{5}{3} [/tex]
