[tex] \dfrac{a}{3} + \dfrac{a-2}{4} = 8[/tex]
Change the denominator to be the same:
[tex] \dfrac{4(a)}{4(3)} + \dfrac{3(a-2)}{3(4)} = 8[/tex]
Simplify:
[tex] \dfrac{4a}{12} + \dfrac{3a-6}{12} = 8[/tex]
Combine into single fraction:
[tex] \dfrac{4a + 3a - 6}{12} = 8[/tex]
Cross multiply:
[tex] \dfrac{7a - 6}{12} = 8[/tex]
Simplify:
[tex]7a - 6= 8 \times 12[/tex]
Evaluate the right side:
[tex]7a - 6= 96[/tex]
Add 6 to both sides:
[tex]7a = 96 + 6[/tex]
Evaluate right side:
[tex]7a = 102[/tex]
Divide by 7 on both sides:
[tex]a = 14 \dfrac{4}{7} [/tex]
