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4\left(x-4\right)-2\left(x+4\right)-\left(x+4\right)=0
Multiply both sides of the equation by 8, the least common multiple of 2,4,8.
4x-16-2\left(x+4\right)-\left(x+4\right)=0
Use the distributive property to multiply 4 by x-4.
4x-16-2x-8-\left(x+4\right)=0
Use the distributive property to multiply -2 by x+4.
2x-16-8-\left(x+4\right)=0
Combine 4x and -2x to get 2x.
2x-24-\left(x+4\right)=0
Subtract 8 from -16 to get -24.
2x-24-x-4=0
To find the opposite of x+4, find the opposite of each term.
x-24-4=0
Combine 2x and -x to get x.
x-28=0
Subtract 4 from -24 to get -28.
x=28
Add 28 to both sides. Anything plus zero gives itself.