Question

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

Answer 1

To solve the equation 17-3(w+5)=6(w+5)-2w, simplify and solve for w by combining like terms and isolating the variable.

Step-by-step explanation:

To solve the equation 17-3(w+5)=6(w+5)-2w, we need to simplify and solve for w. We start by distributing the numbers and variables inside the parentheses:

17 - 3w - 15 = 6w + 30 - 2w

Next, we combine like terms on both sides of the equation:

2 - 3w = 4w + 30

Then, we move all the variables to one side and all the numbers to the other side:

2 - 30 = 4w + 3w

-28 = 7w

Finally, we divide both sides of the equation by 7 to isolate w:

w = -4

Answer 2

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