Solve for x
x=\frac{8}{9}\approx 0.888888889
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4x-24\left(1-\frac{x}{4}\right)=x-16
Multiply both sides of the equation by 8, the least common multiple of 2,4,8.
4x-24\left(1-\frac{x}{4}\right)-x=-16
Subtract x from both sides.
4\left(4x-24\left(1-\frac{x}{4}\right)\right)-4x=-64
Multiply both sides of the equation by 4.
16\left(4x-24\left(1-\frac{x}{4}\right)\right)-16x=-256
Multiply both sides of the equation by 4.
16\left(4x-24+24\times \frac{x}{4}\right)-16x=-256
Use the distributive property to multiply -24 by 1-\frac{x}{4}.
16\left(4x-24+6x\right)-16x=-256
Cancel out 4, the greatest common factor in 24 and 4.
16\left(10x-24\right)-16x=-256
Combine 4x and 6x to get 10x.
160x-384-16x=-256
Use the distributive property to multiply 16 by 10x-24.
144x-384=-256
Combine 160x and -16x to get 144x.
144x=-256+384
Add 384 to both sides.
144x=128
Add -256 and 384 to get 128.
x=\frac{128}{144}
Divide both sides by 144.
x=\frac{8}{9}
Reduce the fraction \frac{128}{144} to lowest terms by extracting and canceling out 16.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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