(28+24.5+x/48+50+48+52)*0.1+8/10*0.15+15/30*0.75>0.5-এর সমাধান করুন

$$( \frac{ 28+24.5+x }{ 48+50+48+52 } ) \times 0.1+ \frac{ 8 }{ 10 } \times 0.15+ \frac{ 15 }{ 30 } \times 0.75 > 0.5$$

Solve for x

$$x>-\frac{213}{5}$$

Solution Steps

Add 28 and 24.5 to get 52.5.

$$\frac{52.5+x}{48+50+48+52}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75>0.5$$

Add 48 and 50 to get 98.

$$\frac{52.5+x}{98+48+52}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75>0.5$$

Add 98 and 48 to get 146.

$$\frac{52.5+x}{146+52}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75>0.5$$

Add 146 and 52 to get 198.

$$\frac{52.5+x}{198}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75>0.5$$

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{52.5+x}{198}\times 0.1+\frac{4}{5}\times 0.15+\frac{15}{30}\times 0.75>0.5$$

Convert decimal number 0.15 to fraction \frac{15}{100}. Reduce the fraction \frac{15}{100} to lowest terms by extracting and canceling out 5.

$$\frac{52.5+x}{198}\times 0.1+\frac{4}{5}\times \frac{3}{20}+\frac{15}{30}\times 0.75>0.5$$

Multiply \frac{4}{5} times \frac{3}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{52.5+x}{198}\times 0.1+\frac{4\times 3}{5\times 20}+\frac{15}{30}\times 0.75>0.5$$

Do the multiplications in the fraction \frac{4\times 3}{5\times 20}.

$$\frac{52.5+x}{198}\times 0.1+\frac{12}{100}+\frac{15}{30}\times 0.75>0.5$$

Reduce the fraction \frac{12}{100} to lowest terms by extracting and canceling out 4.

$$\frac{52.5+x}{198}\times 0.1+\frac{3}{25}+\frac{15}{30}\times 0.75>0.5$$

Reduce the fraction \frac{15}{30} to lowest terms by extracting and canceling out 15.

$$\frac{52.5+x}{198}\times 0.1+\frac{3}{25}+\frac{1}{2}\times 0.75>0.5$$

Convert decimal number 0.75 to fraction \frac{75}{100}. Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{52.5+x}{198}\times 0.1+\frac{3}{25}+\frac{1}{2}\times \frac{3}{4}>0.5$$

Multiply \frac{1}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{52.5+x}{198}\times 0.1+\frac{3}{25}+\frac{1\times 3}{2\times 4}>0.5$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 4}.

$$\frac{52.5+x}{198}\times 0.1+\frac{3}{25}+\frac{3}{8}>0.5$$

Least common multiple of 25 and 8 is 200. Convert \frac{3}{25} and \frac{3}{8} to fractions with denominator 200.

$$\frac{52.5+x}{198}\times 0.1+\frac{24}{200}+\frac{75}{200}>0.5$$

Since \frac{24}{200} and \frac{75}{200} have the same denominator, add them by adding their numerators.

$$\frac{52.5+x}{198}\times 0.1+\frac{24+75}{200}>0.5$$

Add 24 and 75 to get 99.

$$\frac{52.5+x}{198}\times 0.1+\frac{99}{200}>0.5$$

Divide each term of 52.5+x by 198 to get \frac{35}{132}+\frac{1}{198}x.

$$\left(\frac{35}{132}+\frac{1}{198}x\right)\times 0.1+\frac{99}{200}>0.5$$

Use the distributive property to multiply \frac{35}{132}+\frac{1}{198}x by 0.1.

$$\frac{7}{264}+\frac{1}{198}x\times 0.1+\frac{99}{200}>0.5$$

Convert decimal number 0.1 to fraction \frac{1}{10}.

$$\frac{7}{264}+\frac{1}{198}x\times \frac{1}{10}+\frac{99}{200}>0.5$$

Multiply \frac{1}{198} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{264}+\frac{1\times 1}{198\times 10}x+\frac{99}{200}>0.5$$

Do the multiplications in the fraction \frac{1\times 1}{198\times 10}.

$$\frac{7}{264}+\frac{1}{1980}x+\frac{99}{200}>0.5$$

Least common multiple of 264 and 200 is 6600. Convert \frac{7}{264} and \frac{99}{200} to fractions with denominator 6600.

$$\frac{175}{6600}+\frac{1}{1980}x+\frac{3267}{6600}>0.5$$

Since \frac{175}{6600} and \frac{3267}{6600} have the same denominator, add them by adding their numerators.

$$\frac{175+3267}{6600}+\frac{1}{1980}x>0.5$$

Add 175 and 3267 to get 3442.

$$\frac{3442}{6600}+\frac{1}{1980}x>0.5$$

Reduce the fraction \frac{3442}{6600} to lowest terms by extracting and canceling out 2.

$$\frac{1721}{3300}+\frac{1}{1980}x>0.5$$

Subtract \frac{1721}{3300} from both sides.

$$\frac{1}{1980}x>0.5-\frac{1721}{3300}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{1980}x>\frac{1}{2}-\frac{1721}{3300}$$

Least common multiple of 2 and 3300 is 3300. Convert \frac{1}{2} and \frac{1721}{3300} to fractions with denominator 3300.

$$\frac{1}{1980}x>\frac{1650}{3300}-\frac{1721}{3300}$$

Since \frac{1650}{3300} and \frac{1721}{3300} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{1980}x>\frac{1650-1721}{3300}$$

Subtract 1721 from 1650 to get -71.

$$\frac{1}{1980}x>-\frac{71}{3300}$$

Multiply both sides by 1980, the reciprocal of \frac{1}{1980}. Since \frac{1}{1980} is positive, the inequality direction remains the same.

$$x>-\frac{71}{3300}\times 1980$$

Express -\frac{71}{3300}\times 1980 as a single fraction.

$$x>\frac{-71\times 1980}{3300}$$

Multiply -71 and 1980 to get -140580.

$$x>\frac{-140580}{3300}$$

Reduce the fraction \frac{-140580}{3300} to lowest terms by extracting and canceling out 660.

$$x>-\frac{213}{5}$$