1. You have the following equation:
[tex]\frac{9}{2}(8-x)+36=102-\frac{5}{2} (3x+24)[/tex]
2. First, you must apply the Distributive property:
[tex]\frac{72}{2}-\frac{9x}{2}+36=102-\frac{15x}{2}-\frac{120}{2}[/tex]
3. Simplify:
[tex]36}-\frac{9x}{2}+36=102-\frac{15x}{2}-60[/tex]
3. Add the like terms:
[tex]-\frac{9x}{2}+\frac{15x}{2}=102-60-36-36\\ 3x=-30[/tex]
4. Solve for [tex]x[/tex]:
[tex]x=-\frac{30}{3} \\ x=-10[/tex]
Therefore, the answer is: [tex]x=-10[/tex]
