Solve (1/30+1/24)x=1

$$( \frac { 1 } { 30 } + \frac { 1 } { 24 } ) x = 1$$

Solve for x

$$x = \frac{40}{3} = 13\frac{1}{3} \approx 13.333333333$$

Steps for Solving Linear Equation

Least common multiple of 30 and 24 is 120. Convert \frac{1}{30} and \frac{1}{24} to fractions with denominator 120.

$$\left(\frac{4}{120}+\frac{5}{120}\right)x=1$$

Since \frac{4}{120} and \frac{5}{120} have the same denominator, add them by adding their numerators.

$$\frac{4+5}{120}x=1$$

Add 4 and 5 to get 9.

$$\frac{9}{120}x=1$$

Reduce the fraction \frac{9}{120} to lowest terms by extracting and canceling out 3.

$$\frac{3}{40}x=1$$

Multiply both sides by \frac{40}{3}, the reciprocal of \frac{3}{40}.

$$x=1\times \frac{40}{3}$$

Multiply 1 and \frac{40}{3} to get \frac{40}{3}.

$$x=\frac{40}{3}$$