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4x-9+3\left(3-x\right)=2-3x
Multiply both sides of the equation by 6, the least common multiple of 3,2,6.
4x-9+9-3x=2-3x
Use the distributive property to multiply 3 by 3-x.
4x-3x=2-3x
Add -9 and 9 to get 0.
x=2-3x
Combine 4x and -3x to get x.
x+3x=2
Add 3x to both sides.
4x=2
Combine x and 3x to get 4x.
x=\frac{2}{4}
Divide both sides by 4.
x=\frac{1}{2}
Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.