Solve 5(x-9)/4=4(x+9)/5

$$\frac { 5 ( x - 9 ) } { 4 } = \frac { 4 ( x + 9 ) } { 5 }$$

Solve for x

$$x=41$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 4,5.

$$5\times 5\left(x-9\right)=4\times 4\left(x+9\right)$$

Multiply 5 and 5 to get 25.

$$25\left(x-9\right)=4\times 4\left(x+9\right)$$

Use the distributive property to multiply 25 by x-9.

$$25x-225=4\times 4\left(x+9\right)$$

Multiply 4 and 4 to get 16.

$$25x-225=16\left(x+9\right)$$

Use the distributive property to multiply 16 by x+9.

$$25x-225=16x+144$$

Subtract 16x from both sides.

$$25x-225-16x=144$$

Combine 25x and -16x to get 9x.

$$9x-225=144$$

Add 225 to both sides.

$$9x=144+225$$

Add 144 and 225 to get 369.

$$9x=369$$

Divide both sides by 9.

$$x=\frac{369}{9}$$

Divide 369 by 9 to get 41.

$$x=41$$