It is required to solve the equation:
[tex]2\frac{1}{4}+x=5\frac{1}{4}[/tex]To do this, subtract 2 1/4 from both sides of the equation:
[tex]\begin{gathered} 2\frac{1}{4}-2\frac{1}{4}+x=5\frac{1}{4}-2\frac{1}{4} \\ \Rightarrow x=5\frac{1}{4}-2\frac{1}{4} \end{gathered}[/tex]Subtract the mixed fractions on the right:
[tex]\begin{gathered} x=(5+\frac{1}{4})-(2+\frac{1}{4}) \\ \Rightarrow x=5+\frac{1}{4}-2-\frac{1}{4} \\ \Rightarrow x=5-2+\frac{1}{4}-\frac{1}{4} \\ \Rightarrow x=3+0=3 \end{gathered}[/tex]The answer is x=3.