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9\left(x+1\right)=2\left(7x-8\right)
Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by 2\left(x+1\right), the least common multiple of 2,x+1.
9x+9=2\left(7x-8\right)
Use the distributive property to multiply 9 by x+1.
9x+9=14x-16
Use the distributive property to multiply 2 by 7x-8.
9x+9-14x=-16
Subtract 14x from both sides.
-5x+9=-16
Combine 9x and -14x to get -5x.
-5x=-16-9
Subtract 9 from both sides.
-5x=-25
Subtract 9 from -16 to get -25.
x=\frac{-25}{-5}
Divide both sides by -5.
x=5
Divide -25 by -5 to get 5.