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:

$\frac{9}{2}(8-x)+36=102-\frac{5}{2} (3x+24)$

2. First, you must apply the Distributive property:

$\frac{72}{2}-\frac{9x}{2}+36=102-\frac{15x}{2}-\frac{120}{2}$

3. Simplify:

$36}-\frac{9x}{2}+36=102-\frac{15x}{2}-60$

3. Add the like terms:

$-\frac{9x}{2}+\frac{15x}{2}=102-60-36-36\\ 3x=-30$

4. Solve for $x$:

$x=-\frac{30}{3} \\ x=-10$

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