-5(1 – 5x)+5(-8x - 2) = - 4x – 8x
The answers are
X=-5
X=5
No solution
All real answers

x = -5

Step-by-step explanation:

Solve for x:

5 (-8 x - 2) - 5 (1 - 5 x) = -4 x - 8 x

-5 (1 - 5 x) = 25 x - 5:

25 x - 5 + 5 (-8 x - 2) = -4 x - 8 x

5 (-8 x - 2) = -40 x - 10:

25 x + -40 x - 10 - 5 = -4 x - 8 x

Grouping like terms, 25 x - 40 x - 10 - 5 = (25 x - 40 x) + (-5 - 10):

(25 x - 40 x) + (-5 - 10) = -4 x - 8 x

25 x - 40 x = -15 x:

-15 x + (-5 - 10) = -4 x - 8 x

-5 - 10 = -15:

-15 - 15 x = -4 x - 8 x

-4 x - 8 x = -12 x:

-15 x - 15 = -12 x

Add 12 x to both sides:

12 x - 15 x - 15 = 12 x - 12 x

12 x - 12 x = 0:

12 x - 15 x - 15 = 0

12 x - 15 x = -3 x:

-3 x - 15 = 0

Add 15 to both sides:

(15 - 15) - 3 x = 15

15 - 15 = 0:

-3 x = 15

Divide both sides of -3 x = 15 by -3:

(-3 x)/(-3) = 15/(-3)

(-3)/(-3) = 1:

x = 15/(-3)

The gcd of 15 and -3 is 3, so 15/(-3) = (3×5)/(3 (-1)) = 3/3×5/(-1) = 5/(-1):

x = 5/(-1)

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

 x = -5

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