Solve 6(x-11)/5=5(x+11)/6

$$\frac { 6 ( x - 11 ) } { 5 } = \frac { 5 ( x + 11 ) } { 6 }$$

Solve for x

$$x=61$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,6.

$$6\times 6\left(x-11\right)=5\times 5\left(x+11\right)$$

Multiply 6 and 6 to get 36.

$$36\left(x-11\right)=5\times 5\left(x+11\right)$$

Use the distributive property to multiply 36 by x-11.

$$36x-396=5\times 5\left(x+11\right)$$

Multiply 5 and 5 to get 25.

$$36x-396=25\left(x+11\right)$$

Use the distributive property to multiply 25 by x+11.

$$36x-396=25x+275$$

Subtract 25x from both sides.

$$36x-396-25x=275$$

Combine 36x and -25x to get 11x.

$$11x-396=275$$

Add 396 to both sides.

$$11x=275+396$$

Add 275 and 396 to get 671.

$$11x=671$$

Divide both sides by 11.

$$x=\frac{671}{11}$$

Divide 671 by 11 to get 61.

$$x=61$$