What is the complete solution with checking? 10 pts!?

Question

I wanted to find the complete solution with checking with this equation: 2x/3 + 3x/4 = x-5

Answer 1

2x/3 + 3x/4 = x-5

Rewrite the expression with common denominator.

[4(2x) + 3(3x)] / 12 = x - 5.

[8x + 9x] / 12 = x - 5.

17x / 12 = x - 5

Divide each side by 12.

17x = 12(x - 5)

Distribute terms using distributive property:  a( b + c) = ab + ac.

17x = 12x - 60

Subtract 12x from each side.

5x = - 60

Divide each side by 5.

x = - 12.

Check.

2(-12)/3 + 3(-12)/4 = -12 - 5

2(-4) + 3(-3) = - 17

-8 - 9 = - 17

- 17 = - 17.