Answer:
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
