The equation is given to be:
[tex]3x+5x+\frac{1}{6}=\frac{1}{2}[/tex]
Step 1: Multiply each term by 6 to eliminate the fractions
[tex]\begin{gathered} 3x(6)+5x(6)+\frac{1}{6}(6)=\frac{1}{2}(6) \\ 18x+30x+1=3 \end{gathered}[/tex]
Step 2: Add the common terms
[tex]48x+1=3[/tex]
Step 3: Subtract 1 from both sides
[tex]\begin{gathered} 48x+1-1=3-1 \\ 48x=2 \end{gathered}[/tex]
Step 4: Divide both sides of the equation by 48
[tex]\begin{gathered} \frac{48x}{48}=\frac{2}{48} \\ x=\frac{2}{48} \end{gathered}[/tex]
Step 5: Reduce the fraction by dividing through by 2
[tex]\begin{gathered} x=\frac{2\div2}{48\div2} \\ x=\frac{1}{24} \end{gathered}[/tex]
ANSWER
The solution is:
[tex]x=\frac{1}{24}[/tex]
