Solve 1*(1/7.5+1/5)+1/5x=1

$$1 \times ( \frac{ 1 }{ 7.5 } + \frac{ 1 }{ 5 } )+ \frac{ 1 }{ 5 } x=1$$

Solve for x

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

Steps for Solving Linear Equation

Expand \frac{1}{7.5} by multiplying both numerator and the denominator by 10.

$$1\left(\frac{10}{75}+\frac{1}{5}\right)+\frac{1}{5}x=1$$

Reduce the fraction \frac{10}{75} to lowest terms by extracting and canceling out 5.

$$1\left(\frac{2}{15}+\frac{1}{5}\right)+\frac{1}{5}x=1$$

Least common multiple of 15 and 5 is 15. Convert \frac{2}{15} and \frac{1}{5} to fractions with denominator 15.

$$1\left(\frac{2}{15}+\frac{3}{15}\right)+\frac{1}{5}x=1$$

Since \frac{2}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$1\times \frac{2+3}{15}+\frac{1}{5}x=1$$

Add 2 and 3 to get 5.

$$1\times \frac{5}{15}+\frac{1}{5}x=1$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$1\times \frac{1}{3}+\frac{1}{5}x=1$$

Multiply 1 and \frac{1}{3} to get \frac{1}{3}.

$$\frac{1}{3}+\frac{1}{5}x=1$$

Subtract \frac{1}{3} from both sides.

$$\frac{1}{5}x=1-\frac{1}{3}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{1}{5}x=\frac{3}{3}-\frac{1}{3}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}x=\frac{3-1}{3}$$

Subtract 1 from 3 to get 2.

$$\frac{1}{5}x=\frac{2}{3}$$

Multiply both sides by 5, the reciprocal of \frac{1}{5}.

$$x=\frac{2}{3}\times 5$$

Express \frac{2}{3}\times 5 as a single fraction.

$$x=\frac{2\times 5}{3}$$

Multiply 2 and 5 to get 10.

$$x=\frac{10}{3}$$