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5\left(x+1\right)+3\left(x+5\right)=60
Multiply both sides of the equation by 15, the least common multiple of 3,5.
5x+5+3\left(x+5\right)=60
Use the distributive property to multiply 5 by x+1.
5x+5+3x+15=60
Use the distributive property to multiply 3 by x+5.
8x+5+15=60
Combine 5x and 3x to get 8x.
8x+20=60
Add 5 and 15 to get 20.
8x=60-20
Subtract 20 from both sides.
8x=40
Subtract 20 from 60 to get 40.
x=\frac{40}{8}
Divide both sides by 8.
x=5
Divide 40 by 8 to get 5.