The given equation is
[tex]k+2\frac{1}{2}=3\frac{3}{4}[/tex]First, we transform each mixed number into a fraction
[tex]\begin{gathered} k+\frac{2\cdot2+1}{2}=\frac{3\cdot4+3}{4} \\ k+\frac{4+1}{2}=\frac{12+3}{4} \\ k+\frac{5}{2}=\frac{15}{4} \\ k=\frac{15}{4}-\frac{5}{2}=\frac{15\cdot2-4\cdot5}{4\cdot2} \\ k=\frac{30-20}{8}=\frac{10}{8}=\frac{5}{4} \end{gathered}[/tex]Hence, the solution is 5/4.To prove it, we have to replace the variable k for its value of 1/2
[tex]\begin{gathered} \frac{5}{4}+\frac{5}{2}=\frac{15}{4} \\ \frac{5\cdot2+5\cdot4}{4\cdot2}=\frac{15}{4} \\ \frac{10+20}{8}=\frac{15}{4} \\ \frac{30}{8}=\frac{15}{4} \\ \frac{15}{4}=\frac{15}{4} \end{gathered}[/tex]As you can observe, our solution satisfies the equation, which means the answer is correct.
