Solve -6x + 19 = x-2. Check for extraneous solutions.

x = 3

Step-by-step explanation:

Solve -6x + 19 = x-2

Solve for x:

19 - 6 x = x - 2

Subtract x from both sides:

19 + (-6 x - x) = (x - x) - 2

-6 x - x = -7 x:

-7 x + 19 = (x - x) - 2

x - x = 0:

19 - 7 x = -2

Subtract 19 from both sides:

(19 - 19) - 7 x = -19 - 2

19 - 19 = 0:

-7 x = -19 - 2

-19 - 2 = -21:

-7 x = -21

Divide both sides of -7 x = -21 by -7:

(-7 x)/(-7) = (-21)/(-7)

(-7)/(-7) = 1:

x = (-21)/(-7)

The gcd of -21 and -7 is -7, so (-21)/(-7) = (-7×3)/(-7×1) = (-7)/(-7)×3 = 3:

x = 3