What is this problem17-3 (w+5) = 6 (w+5) - 2w

Answer

w = - 4

Step-by-step explanation:

Solve for w:

17 - 3 (w + 5) = 6 (w + 5) - 2 w

-3 (w + 5) = - 3 w - 15:

-3 w - 15 + 17 = 6 (w + 5) - 2 w

Grouping like terms, - 3 w - 15 + 17 = (17 - 15) - 3 w:

(17 - 15) - 3 w = 6 (w + 5) - 2 w

17 - 15 = 2:

2 - 3 w = 6 (w + 5) - 2 w

6 (w + 5) = 6 w + 30:

2 - 3 w = 6 w + 30 - 2 w

Grouping like terms, 6 w - 2 w + 30 = (6 w - 2 w) + 30:

2 - 3 w = (6 w - 2 w) + 30

6 w - 2 w = 4 w:

2 - 3 w = 4 w + 30

Subtract 4 w from both sides:

2 + (-3 w - 4 w) = (4 w - 4 w) + 30

-3 w - 4 w = - 7 w:

-7 w + 2 = (4 w - 4 w) + 30

4 w - 4 w = 0:

2 - 7 w = 30

Subtract 2 from both sides:

(2 - 2) - 7 w = 30 - 2

2 - 2 = 0:

-7 w = 30 - 2

30 - 2 = 28:

-7 w = 28

Divide both sides of - 7 w = 28 by - 7:

(-7 w) / (-7) = 28 / (-7)

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

w = 28 / (-7)

The gcd of 28 and - 7 is 7, so 28 / (-7) = (7*4) / (7 (-1)) = 7/7*4 / (-1) = 4 / (-1):

w = 4 / (-1)

Multiply numerator and denominator of 4 / (-1) by - 1:

Answer: w = - 4