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9\left(x-9\right)=63-7x
Multiply both sides of the equation by 63, the least common multiple of 7,9.
9x-81=63-7x
Use the distributive property to multiply 9 by x-9.
9x-81+7x=63
Add 7x to both sides.
16x-81=63
Combine 9x and 7x to get 16x.
16x=63+81
Add 81 to both sides.
16x=144
Add 63 and 81 to get 144.
x=\frac{144}{16}
Divide both sides by 16.
x=9
Divide 144 by 16 to get 9.