[tex]\frac{1}{10}(x+8)-\frac{1}{15}(x-5)=1[/tex]
Multiply both sides by 30:
[tex]\begin{gathered} 30(\frac{1}{10}(x+8)-\frac{1}{15}(x-5))=30 \\ \frac{30}{10}(x+8)-\frac{30}{15}(x-5)=30 \\ 3(x+8)-2(x-5)=30 \end{gathered}[/tex]
Expand the left hand side using distributive property:
[tex]3x+24-2x+10=30[/tex]
Add like terms:
[tex]x+34=30[/tex]
Subtract 34 from both sides:
[tex]\begin{gathered} x+34-34=30-34 \\ x=-4 \end{gathered}[/tex]
Answer:
x = -4
