Solve 2x<24div627-82^5-[2^4-(18div3)]3

$$2 x < 24 \div 627 - 82 ^ { 5 } - [ 2 ^ { 4 } - ( 18 \div 3 ) ] 3$$

Solve for x

$$x<-\frac{387423139275}{209}$$

Solution Steps

Reduce the fraction \frac{24}{627} to lowest terms by extracting and canceling out 3.

$$2x<\frac{8}{209}-82^{5}-\left(2^{4}-\frac{18}{3}\right)\times 3$$

Calculate 82 to the power of 5 and get 3707398432.

$$2x<\frac{8}{209}-3707398432-\left(2^{4}-\frac{18}{3}\right)\times 3$$

Convert 3707398432 to fraction \frac{774846272288}{209}.

$$2x<\frac{8}{209}-\frac{774846272288}{209}-\left(2^{4}-\frac{18}{3}\right)\times 3$$

Since \frac{8}{209} and \frac{774846272288}{209} have the same denominator, subtract them by subtracting their numerators.

$$2x<\frac{8-774846272288}{209}-\left(2^{4}-\frac{18}{3}\right)\times 3$$

Subtract 774846272288 from 8 to get -774846272280.

$$2x<-\frac{774846272280}{209}-\left(2^{4}-\frac{18}{3}\right)\times 3$$

Calculate 2 to the power of 4 and get 16.

$$2x<-\frac{774846272280}{209}-\left(16-\frac{18}{3}\right)\times 3$$

Divide 18 by 3 to get 6.

$$2x<-\frac{774846272280}{209}-\left(16-6\right)\times 3$$

Subtract 6 from 16 to get 10.

$$2x<-\frac{774846272280}{209}-10\times 3$$

Multiply 10 and 3 to get 30.

$$2x<-\frac{774846272280}{209}-30$$

Convert 30 to fraction \frac{6270}{209}.

$$2x<-\frac{774846272280}{209}-\frac{6270}{209}$$

Since -\frac{774846272280}{209} and \frac{6270}{209} have the same denominator, subtract them by subtracting their numerators.

$$2x<\frac{-774846272280-6270}{209}$$

Subtract 6270 from -774846272280 to get -774846278550.

$$2x<-\frac{774846278550}{209}$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$x<\frac{-\frac{774846278550}{209}}{2}$$

Express \frac{-\frac{774846278550}{209}}{2} as a single fraction.

$$x<\frac{-774846278550}{209\times 2}$$

Multiply 209 and 2 to get 418.

$$x<\frac{-774846278550}{418}$$

Reduce the fraction \frac{-774846278550}{418} to lowest terms by extracting and canceling out 2.

$$x<-\frac{387423139275}{209}$$