Answer:
x=1131/6424
Explanation:
Given the equation:
[tex]$\frac{1}{8}-\frac{5}{7}\left(x-\frac{5}{22}\right)=\frac{4 x}{9}+\frac{1}{12}$[/tex]First, open the bracket:
[tex]\begin{gathered} \frac{1}{8}-\frac{5x}{7}-\frac{5}{7}\left(-\frac{5}{22}\right)=\frac{4 x}{9}+\frac{1}{12} \\ \frac{1}{8}-\frac{5x}{7}+\frac{25}{154}=\frac{4x}{9}+\frac{1}{12} \end{gathered}[/tex]Next, collect like terms:
[tex]\begin{gathered} \text{ Subtract }\frac{1}{12}\text{ from both sides of the equation} \\ \frac{1}{8}-\frac{5x}{7}+\frac{25}{154}-\frac{1}{12}=\frac{4x}{9}+\frac{1}{12}-\frac{1}{12} \\ \begin{equation*} \frac{1}{8}-\frac{5x}{7}+\frac{25}{154}-\frac{1}{12}=\frac{4x}{9} \end{equation*} \\ \text{ Add }\frac{5x}{7}\text{ to both sides of the equation} \\ \frac{1}{8}-\frac{5x}{7}+\frac{5x}{7}+\frac{25}{154}-\frac{1}{12}=\frac{4x}{9}+\frac{5x}{7} \\ \frac{1}{8}+\frac{25}{154}-\frac{1}{12}=\frac{4x}{9}+\frac{5x}{7} \end{gathered}[/tex]Combine the fractions on the left by finding the LCM of 8, 12, and 154.
The LCM of 8, 12, and 154 = 1848
[tex]\begin{gathered} \frac{231(1)+12(25)-154(1)}{1848}=\frac{4x}{9}+\frac{5x}{7} \\ \\ \frac{231+300-154}{1848}=\frac{4x}{9}+\frac{5x}{7} \\ \\ \frac{377}{1848}=\frac{4x}{9}+\frac{5x}{7} \end{gathered}[/tex]
Similarly, combine the fractions on the right by finding the LCM of 9 and 7.
The LCM of 9 and 7 = 63
[tex]\begin{gathered} \frac{377}{1848}=\frac{7(4x)+9(5x)}{9} \\ \\ \frac{377}{1848}=\frac{28x+45x}{63} \\ \\ \frac{377}{1848}=\frac{73x}{63} \end{gathered}[/tex]Finally, cross multiply and solve for x:
[tex]\begin{gathered} 73x\times1848=377\times63 \\ x=\frac{377\times63}{73\times1848} \\ \\ x=\frac{23751}{134904} \\ \\ x=\frac{1131\times21}{6424\times21} \\ \\ x=\frac{1131}{6424} \end{gathered}[/tex]The value of x is 1131/6424.