Start with
[tex]7\left(5x+\dfrac{1}{2}\right)=37x+\dfrac{2}{3}[/tex]
Multiply both sides by 6:
[tex]6\cdot 7\left(5x+\dfrac{1}{2}\right)=6\left(37x+\dfrac{2}{3}\right)[/tex]
On the left hand side, we have
[tex]6\cdot 7\left(5x+\dfrac{1}{2}\right)=42\left(5x+\dfrac{1}{2}\right)[/tex]
And we can distribute the 42 to get
[tex]42\left(5x+\dfrac{1}{2}\right)=210x+21[/tex]
On the right hand side, we have
[tex]6\left(37x+\dfrac{2}{3}\right)=222x+4[/tex]
So, the equation becomes
[tex]210x+21=222x+4[/tex]
Subtract 210x from both sides to get
[tex]21=12x+4[/tex]
Subtract 4 from both sides to get
[tex]17=12x[/tex]
Divide both sides by 12 to get
[tex]x=\dfrac{17}{12}[/tex]
