Solve (1/45+1/60+1/90)x=1

$$( \frac { 1 } { 45 } + \frac { 1 } { 60 } + \frac { 1 } { 90 } ) x = 1$$

Solve for x

$$x=20$$

Steps for Solving Linear Equation

Least common multiple of 45 and 60 is 180. Convert \frac{1}{45} and \frac{1}{60} to fractions with denominator 180.

$$\left(\frac{4}{180}+\frac{3}{180}+\frac{1}{90}\right)x=1$$

Since \frac{4}{180} and \frac{3}{180} have the same denominator, add them by adding their numerators.

$$\left(\frac{4+3}{180}+\frac{1}{90}\right)x=1$$

Add 4 and 3 to get 7.

$$\left(\frac{7}{180}+\frac{1}{90}\right)x=1$$

Least common multiple of 180 and 90 is 180. Convert \frac{7}{180} and \frac{1}{90} to fractions with denominator 180.

$$\left(\frac{7}{180}+\frac{2}{180}\right)x=1$$

Since \frac{7}{180} and \frac{2}{180} have the same denominator, add them by adding their numerators.

$$\frac{7+2}{180}x=1$$

Add 7 and 2 to get 9.

$$\frac{9}{180}x=1$$

Reduce the fraction \frac{9}{180} to lowest terms by extracting and canceling out 9.

$$\frac{1}{20}x=1$$

Multiply both sides by 20, the reciprocal of \frac{1}{20}.

$$x=1\times 20$$

Multiply 1 and 20 to get 20.

$$x=20$$