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9\left(3x-5\right)=4\left(7x+1\right)
Multiply both sides of the equation by 36, the least common multiple of 4,9.
27x-45=4\left(7x+1\right)
Use the distributive property to multiply 9 by 3x-5.
27x-45=28x+4
Use the distributive property to multiply 4 by 7x+1.
27x-45-28x=4
Subtract 28x from both sides.
-x-45=4
Combine 27x and -28x to get -x.
-x=4+45
Add 45 to both sides.
-x=49
Add 4 and 45 to get 49.
x=-49
Multiply both sides by -1.