Question

I will send a picture of the equation hard to type

Answer 1

The given equation is

`k+2(1)/(2)=3(3)/(4)`

First, we transform each mixed number into a fraction

`\begin{gathered} k+(2\cdot2+1)/(2)=(3\cdot4+3)/(4) \\ k+(4+1)/(2)=(12+3)/(4) \\ k+(5)/(2)=(15)/(4) \\ k=(15)/(4)-(5)/(2)=(15\cdot2-4\cdot5)/(4\cdot2) \\ k=(30-20)/(8)=(10)/(8)=(5)/(4) \end{gathered}`Hence, the solution is 5/4.

To prove it, we have to replace the variable k for its value of 1/2

`\begin{gathered} (5)/(4)+(5)/(2)=(15)/(4) \\ (5\cdot2+5\cdot4)/(4\cdot2)=(15)/(4) \\ (10+20)/(8)=(15)/(4) \\ (30)/(8)=(15)/(4) \\ (15)/(4)=(15)/(4) \end{gathered}`

As you can observe, our solution satisfies the equation, which means the answer is correct.