w- 2/5=3 1/2

$${\mathtt{w}}{\mathtt{\,-\,}}{\frac{{\mathtt{2}}}{{\mathtt{5}}}} = {\frac{{\mathtt{7}}}{{\mathtt{2}}}}$$

add 2/5 to both sides

$${\mathtt{w}} = {\frac{{\mathtt{7}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2}}}{{\mathtt{5}}}}$$

Multiply the numerator/deminator of the first fraction by 5, and the numerator/demoninator of the second fraction by 2. We to this to get a common demoniator so we can add the fractions.

$${\mathtt{w}} = {\frac{{\mathtt{35}}}{{\mathtt{10}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{4}}}{{\mathtt{10}}}}$$

$${\mathtt{w}} = {\frac{{\mathtt{39}}}{{\mathtt{10}}}}$$ 

or

w = 3.9

 

Let's check it!

w- 2/5=3 1/2 

3.9- 2/5=3 1/2    ---Imput 3.9 (or 39/10) for w

3.9 - .4 = 3.5     ---Make everything a decimal

3.5 = 3.5 ✔