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5\left(2x-2\right)=7\left(x+2\right)
Multiply both sides of the equation by 35, the least common multiple of 7,5.
10x-10=7\left(x+2\right)
Use the distributive property to multiply 5 by 2x-2.
10x-10=7x+14
Use the distributive property to multiply 7 by x+2.
10x-10-7x=14
Subtract 7x from both sides.
3x-10=14
Combine 10x and -7x to get 3x.
3x=14+10
Add 10 to both sides.
3x=24
Add 14 and 10 to get 24.
x=\frac{24}{3}
Divide both sides by 3.
x=8
Divide 24 by 3 to get 8.