Solve x-1/4-x-5/36=x+5/9

$$\frac{ x-1 }{ 4 } - \frac{ x-5 }{ 36 } = \frac{ x+5 }{ 9 }$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 4,36,9.

$$9\left(x-1\right)-\left(x-5\right)=4\left(x+5\right)$$

Use the distributive property to multiply 9 by x-1.

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

To find the opposite of x-5, find the opposite of each term.

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

The opposite of -5 is 5.

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

Combine 9x and -x to get 8x.

$$8x-9+5=4\left(x+5\right)$$

Add -9 and 5 to get -4.

$$8x-4=4\left(x+5\right)$$

Use the distributive property to multiply 4 by x+5.

$$8x-4=4x+20$$

Subtract 4x from both sides.

$$8x-4-4x=20$$

Combine 8x and -4x to get 4x.

$$4x-4=20$$

Add 4 to both sides.

$$4x=20+4$$

Add 20 and 4 to get 24.

$$4x=24$$

Divide both sides by 4.

$$x=\frac{24}{4}$$

Divide 24 by 4 to get 6.

$$x=6$$