We need to solve the following expression:
[tex]5\frac{1}{2}x+\frac{2}{3}x=37[/tex]
To find which steps are possible we will solve the equation one step at a time and check which of these steps appear on the options.
The first step is to transform the mixed fraction into a improper fraction, we do that by adding the integer part wih the fraction part.
[tex]\begin{gathered} (5+\frac{1}{2})x+\frac{2}{3}x=37 \\ (\frac{2\cdot5+1}{2})x+\frac{2}{3}x=37 \\ (\frac{10+1}{2})x+\frac{2}{3}x=37 \\ \frac{11}{2}x+\frac{2}{3}x=37 \end{gathered}[/tex]
The second step is to find the LCM of the two fractions and add them.
[tex]\begin{gathered} \frac{11\cdot3\cdot x+2\cdot2\cdot x}{6}=37 \\ \frac{33x+4x}{6}=37 \\ \frac{37x}{6}=37 \end{gathered}[/tex]
The third step is to multiply both sides by 6.
[tex]\begin{gathered} \frac{37x}{6}\cdot6=37\cdot6 \\ 37x=222 \end{gathered}[/tex]
The fourth step is to divide both sides by 37.
[tex]\begin{gathered} \frac{37}{37}x=\frac{222}{37} \\ x=6 \end{gathered}[/tex]
The first, second and fourth step appear on the options. Therefore we should marke the option "x=6", the option "37/6 x=37" and the option "11/2 x + 2/3 x= 37".
