What value of x makes the equation 3 (x-6) - 8x=-2+5 (2x+1) true?

x = (-7) / 5

Step-by-step explanation:

Solve for x:

3 (x - 6) - 8 x = 5 (2 x + 1) - 2

3 (x - 6) = 3 x - 18:

3 x - 18 - 8 x = 5 (2 x + 1) - 2

Grouping like terms, 3 x - 8 x - 18 = (3 x - 8 x) - 18:

(3 x - 8 x) - 18 = 5 (2 x + 1) - 2

3 x - 8 x = - 5 x:

-5 x - 18 = 5 (2 x + 1) - 2

5 (2 x + 1) = 10 x + 5:

-5 x - 18 = 10 x + 5 - 2

Add like terms. 5 - 2 = 3:

-5 x - 18 = 10 x + 3

Subtract 10 x from both sides:

(-5 x - 10 x) - 18 = (10 x - 10 x) + 3

-5 x - 10 x = - 15 x:

-15 x - 18 = (10 x - 10 x) + 3

10 x - 10 x = 0:

-15 x - 18 = 3

Add 18 to both sides:

(18 - 18) - 15 x = 18 + 3

18 - 18 = 0:

-15 x = 3 + 18

3 + 18 = 21:

-15 x = 21

Divide both sides of - 15 x = 21 by - 15:

(-15 x) / (-15) = 21 / (-15)

(-15) / (-15) = 1:

x = 21 / (-15)

The gcd of 21 and - 15 is 3, so 21 / (-15) = (3*7) / (3 (-5)) = 3/3*7 / (-5) = 7 / (-5):

x = 7 / (-5)

Multiply numerator and denominator of 7 / (-5) by - 1:

Answer: x = (-7) / 5