Solve for x
x=\frac{5}{7}\approx 0.714285714
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30\left(x-1\right)-20\left(x-2\right)-15\left(x-3\right)=12\left(5-x\right)
Multiply both sides of the equation by 60, the least common multiple of 2,3,4,5.
30x-30-20\left(x-2\right)-15\left(x-3\right)=12\left(5-x\right)
Use the distributive property to multiply 30 by x-1.
30x-30-20x+40-15\left(x-3\right)=12\left(5-x\right)
Use the distributive property to multiply -20 by x-2.
10x-30+40-15\left(x-3\right)=12\left(5-x\right)
Combine 30x and -20x to get 10x.
10x+10-15\left(x-3\right)=12\left(5-x\right)
Add -30 and 40 to get 10.
10x+10-15x+45=12\left(5-x\right)
Use the distributive property to multiply -15 by x-3.
-5x+10+45=12\left(5-x\right)
Combine 10x and -15x to get -5x.
-5x+55=12\left(5-x\right)
Add 10 and 45 to get 55.
-5x+55=60-12x
Use the distributive property to multiply 12 by 5-x.
-5x+55+12x=60
Add 12x to both sides.
7x+55=60
Combine -5x and 12x to get 7x.
7x=60-55
Subtract 55 from both sides.
7x=5
Subtract 55 from 60 to get 5.
x=\frac{5}{7}
Divide both sides by 7.
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