Combining like terms, move the one with coefficient a to the left, and move the constant to the right
[tex] \dfrac{a}{2} - \dfrac{2}{3} =a+ \dfrac{1}{5} [/tex]
[tex] \dfrac{a}{2} - a =\dfrac{1}{5} + \dfrac{2}{3}[/tex]
equalize the denominators in like-terms
[tex] \dfrac{a}{2} - \dfrac{2a}{2} =\dfrac{1 \times 3}{5 \times 3} + \dfrac{2 \times 5}{3 \times 5}[/tex]
[tex]\dfrac{a}{2} - \dfrac{2a}{2} =\dfrac{3}{15} + \dfrac{10}{15}[/tex]
do the operation to the numerators
[tex]\dfrac{-a}{2} =\dfrac{13}{15}[/tex]
solve for a
-a = [tex]\dfrac{13}{15} \times 2[/tex]
-a = [tex]\dfrac{26}{15}[/tex]
a = [tex]- \dfrac{26}{15}[/tex]
