Solve for x
x = \frac{5}{2} = 2\frac{1}{2} = 2.5
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15\left(2x-2\right)=10\left(3x-6\right)-6\left(4x-15\right)
Multiply both sides of the equation by 30, the least common multiple of 2,3,5.
30x-30=10\left(3x-6\right)-6\left(4x-15\right)
Use the distributive property to multiply 15 by 2x-2.
30x-30=30x-60-6\left(4x-15\right)
Use the distributive property to multiply 10 by 3x-6.
30x-30=30x-60-24x+90
Use the distributive property to multiply -6 by 4x-15.
30x-30=6x-60+90
Combine 30x and -24x to get 6x.
30x-30=6x+30
Add -60 and 90 to get 30.
30x-30-6x=30
Subtract 6x from both sides.
24x-30=30
Combine 30x and -6x to get 24x.
24x=30+30
Add 30 to both sides.
24x=60
Add 30 and 30 to get 60.
x=\frac{60}{24}
Divide both sides by 24.
x=\frac{5}{2}
Reduce the fraction \frac{60}{24} to lowest terms by extracting and canceling out 12.
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