To solve the linear equation 1-2(x-1)=4(3-x)+2x, we will simplify and solve for x.

First, let’s simplify the equation step by step:

1-2(x-1) = 4(3-x) + 2x

Distribute the -2 and 4:

1 - 2x + 2 = 12 - 4x + 2x

Combine like terms:

3 - 2x = 12 - 2x

Now, let’s isolate the variable x:

Add 2x to both sides:

3 - 2x + 2x = 12 - 2x + 2x

3 = 12

Since 3 does not equal 12, this equation has no solution.

Therefore, the equation 1-2(x-1)=4(3-x)+2x has no solution.