Answer
Elena must have substracted 1/2x from both sides of the equation.
Lin must have multiplied both sides of the equation by 2
Explanation
The equation given is
[tex]\frac{1}{2}x+3=\frac{7}{2}x+5[/tex]
For Elena to have arrived at
[tex]3=\frac{7}{2}x-\frac{1}{2}x+5[/tex]
Then Elena must have substracted 1/2x from both sides of the equation.
That is;
[tex]\begin{gathered} \frac{1}{2}x+3=\frac{7}{2}x+5 \\ \text{Substracting }\frac{1}{2}x\text{ from both sides of the equation will give Elena first step} \\ \frac{1}{2}x+3-\frac{1}{2}x=\frac{7}{2}x+5-\frac{1}{2}x \\ 3=\frac{7}{2}x-\frac{1}{2}x+5 \end{gathered}[/tex]
For Lin to have arrived at
[tex]x+6=7x+10[/tex]
It shows Lin must have multiplied both sides of the equation by 2
That is;
[tex]\begin{gathered} \frac{1}{2}x+3=\frac{7}{2}x+5 \\ \text{Multiply both sides of the equation by the lowest common mutiple } \\ \text{of the denominator which is 2.} \\ \frac{1}{2}x(2)+3(2)=\frac{7}{2}x(2)+5(2) \\ x+6=7x+10 \end{gathered}[/tex]
