5 (x+4) + 10-2x+3 (2x+9)

x = (-19) / 3

Step-by-step explanation:

Solve for x:

10 - 2 x + 5 (x + 4) + 3 (2 x + 9) = 0

5 (x + 4) = 5 x + 20:

10 - 2 x + 5 x + 20 + 3 (2 x + 9) = 0

3 (2 x + 9) = 6 x + 27:

6 x + 27 + 5 x - 2 x + 10 + 20 = 0

Grouping like terms, 6 x + 5 x - 2 x + 10 + 20 + 27 = (-2 x + 5 x + 6 x) + (10 + 20 + 27):

(-2 x + 5 x + 6 x) + (10 + 20 + 27) = 0

-2 x + 5 x + 6 x = 9 x:

9 x + (10 + 20 + 27) = 0

10 + 20 + 27 = 57:

9 x + 57 = 0

Subtract 57 from both sides:

9 x + (57 - 57) = - 57

57 - 57 = 0:

9 x = - 57

Divide both sides of 9 x = - 57 by 9:

(9 x) / 9 = (-57) / 9

9/9 = 1:

x = (-57) / 9

The gcd of 57 and 9 is 3, so (-57) / 9 = ( - (3*19)) / (3*3) = 3/3 * (-19) / 3 = (-19) / 3:

Answer: x = (-19) / 3