Solve 9(330-4x)(5/4)^20+4xgeq4*330

$$9 ( 330 - 4 x ) ( \frac { 5 } { 4 } ) ^ { 20 } + 4 x \geq 4 \times 330$$

Solve for x

$$x\leq \frac{140894958311995965}{1714414746275698}$$

Solution Steps

Calculate \frac{5}{4} to the power of 20 and get \frac{95367431640625}{1099511627776}.

$$9\left(330-4x\right)\times \frac{95367431640625}{1099511627776}+4x\geq 4\times 330$$

Express 9\times \frac{95367431640625}{1099511627776} as a single fraction.

$$\frac{9\times 95367431640625}{1099511627776}\left(330-4x\right)+4x\geq 4\times 330$$

Multiply 9 and 95367431640625 to get 858306884765625.

$$\frac{858306884765625}{1099511627776}\left(330-4x\right)+4x\geq 4\times 330$$

Use the distributive property to multiply \frac{858306884765625}{1099511627776} by 330-4x.

$$\frac{858306884765625}{1099511627776}\times 330+\frac{858306884765625}{1099511627776}\left(-4\right)x+4x\geq 4\times 330$$

Express \frac{858306884765625}{1099511627776}\times 330 as a single fraction.

$$\frac{858306884765625\times 330}{1099511627776}+\frac{858306884765625}{1099511627776}\left(-4\right)x+4x\geq 4\times 330$$

Multiply 858306884765625 and 330 to get 283241271972656250.

$$\frac{283241271972656250}{1099511627776}+\frac{858306884765625}{1099511627776}\left(-4\right)x+4x\geq 4\times 330$$

Reduce the fraction \frac{283241271972656250}{1099511627776} to lowest terms by extracting and canceling out 2.

$$\frac{141620635986328125}{549755813888}+\frac{858306884765625}{1099511627776}\left(-4\right)x+4x\geq 4\times 330$$

Express \frac{858306884765625}{1099511627776}\left(-4\right) as a single fraction.

$$\frac{141620635986328125}{549755813888}+\frac{858306884765625\left(-4\right)}{1099511627776}x+4x\geq 4\times 330$$

Multiply 858306884765625 and -4 to get -3433227539062500.

$$\frac{141620635986328125}{549755813888}+\frac{-3433227539062500}{1099511627776}x+4x\geq 4\times 330$$

Reduce the fraction \frac{-3433227539062500}{1099511627776} to lowest terms by extracting and canceling out 4.

$$\frac{141620635986328125}{549755813888}-\frac{858306884765625}{274877906944}x+4x\geq 4\times 330$$

Combine -\frac{858306884765625}{274877906944}x and 4x to get -\frac{857207373137849}{274877906944}x.

$$\frac{141620635986328125}{549755813888}-\frac{857207373137849}{274877906944}x\geq 4\times 330$$

Multiply 4 and 330 to get 1320.

$$\frac{141620635986328125}{549755813888}-\frac{857207373137849}{274877906944}x\geq 1320$$

Subtract \frac{141620635986328125}{549755813888} from both sides.

$$-\frac{857207373137849}{274877906944}x\geq 1320-\frac{141620635986328125}{549755813888}$$

Convert 1320 to fraction \frac{725677674332160}{549755813888}.

$$-\frac{857207373137849}{274877906944}x\geq \frac{725677674332160}{549755813888}-\frac{141620635986328125}{549755813888}$$

Since \frac{725677674332160}{549755813888} and \frac{141620635986328125}{549755813888} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{857207373137849}{274877906944}x\geq \frac{725677674332160-141620635986328125}{549755813888}$$

Subtract 141620635986328125 from 725677674332160 to get -140894958311995965.

$$-\frac{857207373137849}{274877906944}x\geq -\frac{140894958311995965}{549755813888}$$

Multiply both sides by -\frac{274877906944}{857207373137849}, the reciprocal of -\frac{857207373137849}{274877906944}. Since -\frac{857207373137849}{274877906944} is negative, the inequality direction is changed.

$$x\leq -\frac{140894958311995965}{549755813888}\left(-\frac{274877906944}{857207373137849}\right)$$

Multiply -\frac{140894958311995965}{549755813888} times -\frac{274877906944}{857207373137849} by multiplying numerator times numerator and denominator times denominator.

$$x\leq \frac{-140894958311995965\left(-274877906944\right)}{549755813888\times 857207373137849}$$

Do the multiplications in the fraction \frac{-140894958311995965\left(-274877906944\right)}{549755813888\times 857207373137849}.

$$x\leq \frac{38728911239763586186173480960}{471254737090192685412646912}$$

Reduce the fraction \frac{38728911239763586186173480960}{471254737090192685412646912} to lowest terms by extracting and canceling out 274877906944.

$$x\leq \frac{140894958311995965}{1714414746275698}$$