Question

solve the equation for x. show each step of the solution. name the justification for each step of the solution 9/2 (8-x) +36=102-5/2(3x+24)

Answer 1

1. You have the following equation:

`(9)/(2)(8-x)+36=102-(5)/(2) (3x+24)`

2. First, you must apply the Distributive property:

`(72)/(2)-(9x)/(2)+36=102-(15x)/(2)-(120)/(2)`

3. Simplify:

`36}-(9x)/(2)+36=102-(15x)/(2)-60`

3. Add the like terms:

`-(9x)/(2)+(15x)/(2)=102-60-36-36\\ 3x=-30`

4. Solve for
`x`:

`x=-(30)/(3) \\ x=-10`

Therefore, the answer is:
`x=-10`