Solve 1=(1/2+1/3+1/4+1/5)x

$$1 = ( \frac{ 1 }{ 2 } + \frac{ 1 }{ 3 } + \frac{ 1 }{ 4 } + \frac{ 1 }{ 5 } )x$$

Solve for x

$$x=\frac{60}{77}\approx 0.779220779$$

Steps for Solving Linear Equation

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$1=\left(\frac{3}{6}+\frac{2}{6}+\frac{1}{4}+\frac{1}{5}\right)x$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$1=\left(\frac{3+2}{6}+\frac{1}{4}+\frac{1}{5}\right)x$$

Add 3 and 2 to get 5.

$$1=\left(\frac{5}{6}+\frac{1}{4}+\frac{1}{5}\right)x$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.

$$1=\left(\frac{10}{12}+\frac{3}{12}+\frac{1}{5}\right)x$$

Since \frac{10}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$1=\left(\frac{10+3}{12}+\frac{1}{5}\right)x$$

Add 10 and 3 to get 13.

$$1=\left(\frac{13}{12}+\frac{1}{5}\right)x$$

Least common multiple of 12 and 5 is 60. Convert \frac{13}{12} and \frac{1}{5} to fractions with denominator 60.

$$1=\left(\frac{65}{60}+\frac{12}{60}\right)x$$

Since \frac{65}{60} and \frac{12}{60} have the same denominator, add them by adding their numerators.

$$1=\frac{65+12}{60}x$$

Add 65 and 12 to get 77.

$$1=\frac{77}{60}x$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{77}{60}x=1$$

Multiply both sides by \frac{60}{77}, the reciprocal of \frac{77}{60}.

$$x=1\times \frac{60}{77}$$

Multiply 1 and \frac{60}{77} to get \frac{60}{77}.

$$x=\frac{60}{77}$$