Solve 17/30(x+3)=17/50(x+10)

$$\frac { 17 } { 30 } ( x + 3 ) = \frac { 17 } { 50 } ( x + 10 )$$

Solve for x

$$x = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{17}{30} by x+3.

$$\frac{17}{30}x+\frac{17}{30}\times 3=\frac{17}{50}\left(x+10\right)$$

Express \frac{17}{30}\times 3 as a single fraction.

$$\frac{17}{30}x+\frac{17\times 3}{30}=\frac{17}{50}\left(x+10\right)$$

Multiply 17 and 3 to get 51.

$$\frac{17}{30}x+\frac{51}{30}=\frac{17}{50}\left(x+10\right)$$

Reduce the fraction \frac{51}{30} to lowest terms by extracting and canceling out 3.

$$\frac{17}{30}x+\frac{17}{10}=\frac{17}{50}\left(x+10\right)$$

Use the distributive property to multiply \frac{17}{50} by x+10.

$$\frac{17}{30}x+\frac{17}{10}=\frac{17}{50}x+\frac{17}{50}\times 10$$

Express \frac{17}{50}\times 10 as a single fraction.

$$\frac{17}{30}x+\frac{17}{10}=\frac{17}{50}x+\frac{17\times 10}{50}$$

Multiply 17 and 10 to get 170.

$$\frac{17}{30}x+\frac{17}{10}=\frac{17}{50}x+\frac{170}{50}$$

Reduce the fraction \frac{170}{50} to lowest terms by extracting and canceling out 10.

$$\frac{17}{30}x+\frac{17}{10}=\frac{17}{50}x+\frac{17}{5}$$

Subtract \frac{17}{50}x from both sides.

$$\frac{17}{30}x+\frac{17}{10}-\frac{17}{50}x=\frac{17}{5}$$

Combine \frac{17}{30}x and -\frac{17}{50}x to get \frac{17}{75}x.

$$\frac{17}{75}x+\frac{17}{10}=\frac{17}{5}$$

Subtract \frac{17}{10} from both sides.

$$\frac{17}{75}x=\frac{17}{5}-\frac{17}{10}$$

Least common multiple of 5 and 10 is 10. Convert \frac{17}{5} and \frac{17}{10} to fractions with denominator 10.

$$\frac{17}{75}x=\frac{34}{10}-\frac{17}{10}$$

Since \frac{34}{10} and \frac{17}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{75}x=\frac{34-17}{10}$$

Subtract 17 from 34 to get 17.

$$\frac{17}{75}x=\frac{17}{10}$$

Multiply both sides by \frac{75}{17}, the reciprocal of \frac{17}{75}.

$$x=\frac{17}{10}\times \frac{75}{17}$$

Multiply \frac{17}{10} times \frac{75}{17} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{17\times 75}{10\times 17}$$

Cancel out 17 in both numerator and denominator.

$$x=\frac{75}{10}$$

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

$$x=\frac{15}{2}$$