Solve 5/6(2x+14)=7/12(3x+20)

$$\frac { 5 } { 6 } ( 2 x + 14 ) = \frac { 7 } { 12 } ( 3 x + 20 )$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{5}{6} by 2x+14.

$$\frac{5}{6}\times 2x+\frac{5}{6}\times 14=\frac{7}{12}\left(3x+20\right)$$

Express \frac{5}{6}\times 2 as a single fraction.

$$\frac{5\times 2}{6}x+\frac{5}{6}\times 14=\frac{7}{12}\left(3x+20\right)$$

Multiply 5 and 2 to get 10.

$$\frac{10}{6}x+\frac{5}{6}\times 14=\frac{7}{12}\left(3x+20\right)$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{3}x+\frac{5}{6}\times 14=\frac{7}{12}\left(3x+20\right)$$

Express \frac{5}{6}\times 14 as a single fraction.

$$\frac{5}{3}x+\frac{5\times 14}{6}=\frac{7}{12}\left(3x+20\right)$$

Multiply 5 and 14 to get 70.

$$\frac{5}{3}x+\frac{70}{6}=\frac{7}{12}\left(3x+20\right)$$

Reduce the fraction \frac{70}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{3}x+\frac{35}{3}=\frac{7}{12}\left(3x+20\right)$$

Use the distributive property to multiply \frac{7}{12} by 3x+20.

$$\frac{5}{3}x+\frac{35}{3}=\frac{7}{12}\times 3x+\frac{7}{12}\times 20$$

Express \frac{7}{12}\times 3 as a single fraction.

$$\frac{5}{3}x+\frac{35}{3}=\frac{7\times 3}{12}x+\frac{7}{12}\times 20$$

Multiply 7 and 3 to get 21.

$$\frac{5}{3}x+\frac{35}{3}=\frac{21}{12}x+\frac{7}{12}\times 20$$

Reduce the fraction \frac{21}{12} to lowest terms by extracting and canceling out 3.

$$\frac{5}{3}x+\frac{35}{3}=\frac{7}{4}x+\frac{7}{12}\times 20$$

Express \frac{7}{12}\times 20 as a single fraction.

$$\frac{5}{3}x+\frac{35}{3}=\frac{7}{4}x+\frac{7\times 20}{12}$$

Multiply 7 and 20 to get 140.

$$\frac{5}{3}x+\frac{35}{3}=\frac{7}{4}x+\frac{140}{12}$$

Reduce the fraction \frac{140}{12} to lowest terms by extracting and canceling out 4.

$$\frac{5}{3}x+\frac{35}{3}=\frac{7}{4}x+\frac{35}{3}$$

Subtract \frac{7}{4}x from both sides.

$$\frac{5}{3}x+\frac{35}{3}-\frac{7}{4}x=\frac{35}{3}$$

Combine \frac{5}{3}x and -\frac{7}{4}x to get -\frac{1}{12}x.

$$-\frac{1}{12}x+\frac{35}{3}=\frac{35}{3}$$

Subtract \frac{35}{3} from both sides.

$$-\frac{1}{12}x=\frac{35}{3}-\frac{35}{3}$$

Subtract \frac{35}{3} from \frac{35}{3} to get 0.

$$-\frac{1}{12}x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -\frac{1}{12} is not equal to 0, x must be equal to 0.

$$x=0$$