Question

-2(4w-6)+6w=4 (w+4)

Answer 1

It's going to take a moment for me to write it out :P

Answer 2

-8w+12+6w=4w+16
-2w+12=4w+16
-6w=4
w=-4/6

Answer 3

Distribute -2 over \(4 w-6.\)
\(-2 (4 w-6) = 12-8 w:\)
\(6 w+12-8 w = 4 (w+4)\)
Group like terms in \(6 w-8 w+12.\)
Grouping like terms, \(6 w-8 w+12 = 12+(6 w-8 w):\)
\(12+(6 w-8 w) = 4 (w+4)\)
Combine like terms in 6 w-8 w.
\(w-8 w = -2 w:\)
\(-2 w+12 = 4 (w+4)\)
Write the linear polynomial on the left hand side in standard form.
Expand out terms of the right hand side:
\(12-2 w = 4 w+16\)
Move terms with w to the left hand side.
Subtract 4 w from both sides:
\(12+(-2 w-4 w) = (4 w-4 w)+16\)
Combine like terms in \(-2 w-4 w.\)
\(-2 w-4 w = -6 w:\)
\(-6 w+12 = (4 w-4 w)+16\)
Look for two terms that sum to zero.
\(4 w-4 w = 0:\)
\(12-6 w = 16\)
Isolate terms with w to the left hand side.
Subtract 12 from both sides:
\((12-12)-6 w = 16-12\)
Look for two terms that sum to zero.
\(12-12 = 0:\)
\(-6 w = 16-12\)
Evaluate \(16-12.\)
\(16-12 = 4:\)
\(-6 w = 4\)
Divide both sides by a constant to simplify the equation.
Divide both sides of \(-6 w = 4\) by -6:
\(\frac{-6 w}{-6} = \frac{4}{-6}\)
Any nonzero number divided by itself is one.
\(\frac{-6}{-6} = 1:\)
\(w = \frac{4}{-6}\)
Reduce \(\frac{4}{-6}\) to lowest terms. Start by finding the GCD of 4 and -6.
The gcd of 4 and -6 is 2, so \(\frac{4}{-6} = \frac{2×2}{2 (-3)} = \frac{2}{2}×\frac{2}{-3} = \frac{2}{-3}\):
w = 2/(-3)
Simplify the sign of \(\frac{2}{-3}\).
Multiply numerator and denominator of \(\frac{2}{-3}\) by -1:

Answer 4

I don't know why I still work so hard to explain this crap when no one cares enough about their education to pay attention :/