Solve for x
x=0
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8x-4x-1=2\left(x-\frac{1}{2}\right)
To find the opposite of 4x+1, find the opposite of each term.
4x-1=2\left(x-\frac{1}{2}\right)
Combine 8x and -4x to get 4x.
4x-1=2x+2\left(-\frac{1}{2}\right)
Use the distributive property to multiply 2 by x-\frac{1}{2}.
4x-1=2x-1
Cancel out 2 and 2.
4x-1-2x=-1
Subtract 2x from both sides.
2x-1=-1
Combine 4x and -2x to get 2x.
2x=-1+1
Add 1 to both sides.
2x=0
Add -1 and 1 to get 0.
x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since 2 is not equal to 0, x must be equal to 0.
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