Answer:
[tex]x=-8\frac{1}{3}[/tex]Explanation:
Given the equation
[tex]\frac{1}{5}x+\frac{1}{2}=3+\frac{1}{2}x[/tex]We begin by collecting like terms as follows:
[tex]\frac{1}{5}x-\frac{1}{2}x=3-\frac{1}{2}[/tex]Next, we take the lowest common multiples of the denominator on each side.
[tex]\begin{gathered} \frac{2x-5x}{10}=\frac{6-1}{2} \\ -\frac{3x}{10}=\frac{5}{2} \end{gathered}[/tex]We cross-multiply
[tex]\begin{gathered} -3x\times2=10\times5 \\ -6x=50 \end{gathered}[/tex]Finally, apply the division rule of equality.
[tex]\begin{gathered} -\frac{6x}{-6}=\frac{50}{-6} \\ x=-8\frac{2}{6} \\ x=-8\frac{1}{3} \end{gathered}[/tex]