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6\times 3+6\left(x+1\right)\left(-\frac{1}{2}\right)=2
Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by 6\left(x+1\right), the least common multiple of x+1,2,3x+3.
18+6\left(x+1\right)\left(-\frac{1}{2}\right)=2
Multiply 6 and 3 to get 18.
18-3\left(x+1\right)=2
Multiply 6 and -\frac{1}{2} to get -3.
18-3x-3=2
Use the distributive property to multiply -3 by x+1.
15-3x=2
Subtract 3 from 18 to get 15.
-3x=2-15
Subtract 15 from both sides.
-3x=-13
Subtract 15 from 2 to get -13.
x=\frac{-13}{-3}
Divide both sides by -3.
x=\frac{13}{3}
Fraction \frac{-13}{-3} can be simplified to \frac{13}{3} by removing the negative sign from both the numerator and the denominator.