Question

Please help! This assignment is due soon! (In The photo)

Answer 1

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

$\frac{1}{2}x+3=\frac{7}{2}x+5$

For Elena to have arrived at

$3=\frac{7}{2}x-\frac{1}{2}x+5$

Then Elena must have substracted 1/2x from both sides of the equation.

That is;

$\begin{gathered} \frac{1}{2}x+3=\frac{7}{2}x+5 \\ \text{Substracting }\frac{1}{2}x\text{ from both sides of the equation will give Elena first step} \\ \frac{1}{2}x+3-\frac{1}{2}x=\frac{7}{2}x+5-\frac{1}{2}x \\ 3=\frac{7}{2}x-\frac{1}{2}x+5 \end{gathered}$

For Lin to have arrived at

$x+6=7x+10$

It shows Lin must have multiplied both sides of the equation by 2

That is;

$\begin{gathered} \frac{1}{2}x+3=\frac{7}{2}x+5 \\ \text{Multiply both sides of the equation by the lowest common mutiple } \\ \text{of the denominator which is 2.} \\ \frac{1}{2}x(2)+3(2)=\frac{7}{2}x(2)+5(2) \\ x+6=7x+10 \end{gathered}$