[tex] \frac{1}{2} w + 7 = 2w - 2[/tex]
First, replace the numerator with 'w'.
[tex] \frac{w}{2} +7=2w-2[/tex]
Second, multiply both sides by 2.
[tex]w + 14 = 4w - 2[/tex]
Third, subtract 'w' from both sides.
[tex]14 = 4w - 4 - w[/tex]
Fourth, simplify to 3w - 4.
[tex]14 = 3w - 4[/tex]
Fifth, add '4' to both sides.
[tex]14+4=3w[/tex]
Sixth, add 14 + 4.
[tex]18 = 3w[/tex]
Seventh, divide both sides by '3'.
[tex] \frac{18}{3} =w[/tex]
Eighth, since 6 goes into 3 to get 18, simplify the fraction to 6.
[tex]6 = w[/tex]
Ninth, switch the sides.
[tex]w = 6[/tex]
Answer: w = 6
