Solve for x
x=-1
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5\left(x+7\right)-3\left(3x-2\right)=45
Multiply both sides of the equation by 15, the least common multiple of 3,5.
5x+35-3\left(3x-2\right)=45
Use the distributive property to multiply 5 by x+7.
5x+35-9x+6=45
Use the distributive property to multiply -3 by 3x-2.
-4x+35+6=45
Combine 5x and -9x to get -4x.
-4x+41=45
Add 35 and 6 to get 41.
-4x=45-41
Subtract 41 from both sides.
-4x=4
Subtract 41 from 45 to get 4.
x=\frac{4}{-4}
Divide both sides by -4.
x=-1
Divide 4 by -4 to get -1.
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