Solve for x: - 13 = 5 (1 + 4x) - 2x

x = - 1

Step-by-step explanation:

Solve for x:

-13 = 5 (4 x + 1) - 2 x

5 (4 x + 1) = 20 x + 5:

-13 = 20 x + 5 - 2 x

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

-13 = (-2 x + 20 x) + 5

20 x - 2 x = 18 x:

-13 = 18 x + 5

-13 = 18 x + 5 is equivalent to 18 x + 5 = - 13:

18 x + 5 = - 13

Subtract 5 from both sides:

18 x + (5 - 5) = - 5 - 13

5 - 5 = 0:

18 x = - 5 - 13

-5 - 13 = - 18:

18 x = - 18

Divide both sides of 18 x = - 18 by 18:

(18 x) / 18 = (-18) / 18

18/18 = 1:

x = (-18) / 18

The gcd of - 18 and 18 is 18, so (-18) / 18 = (18 (-1)) / (18*1) = 18/18*-1 = - 1:

Answer: x = - 1