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3\left(1+2x\right)+5\left(4-x\right)=1
Multiply both sides of the equation by 15, the least common multiple of 5,3,15.
3+6x+5\left(4-x\right)=1
Use the distributive property to multiply 3 by 1+2x.
3+6x+20-5x=1
Use the distributive property to multiply 5 by 4-x.
23+6x-5x=1
Add 3 and 20 to get 23.
23+x=1
Combine 6x and -5x to get x.
x=1-23
Subtract 23 from both sides.
x=-22
Subtract 23 from 1 to get -22.