The given equation is,
[tex]4.5(8-x)+22=102-2.5(5x+24)[/tex]
Solving for x
Expanding both sides of the equation
[tex]\begin{gathered} 4.5\times8+4.5\times-x+22=102-2.5\times5x-2.5\times24 \\ 36+22-4.5x=102-12.5x-60 \\ 58-4.5x=102-60-12.5x \\ 58-4.5x=42-12.5x \end{gathered}[/tex]
Collect like terms
[tex]\begin{gathered} -4.5x+12.5x=42-58 \\ 8x=-16 \end{gathered}[/tex]
Divide both sides by 8
[tex]\begin{gathered} \frac{8x}{8}=-\frac{16}{8} \\ x=-2 \end{gathered}[/tex]
Hence,
[tex]x=-2[/tex]
