Solve x+3/2-5x-1/6=1

$$\frac{ x+3 }{ 2 } - \frac{ 5x-1 }{ 6 } =1$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,6.

$$3\left(x+3\right)-\left(5x-1\right)=6$$

Use the distributive property to multiply 3 by x+3.

$$3x+9-\left(5x-1\right)=6$$

To find the opposite of 5x-1, find the opposite of each term.

$$3x+9-5x-\left(-1\right)=6$$

The opposite of -1 is 1.

$$3x+9-5x+1=6$$

Combine 3x and -5x to get -2x.

$$-2x+9+1=6$$

Add 9 and 1 to get 10.

$$-2x+10=6$$

Subtract 10 from both sides.

$$-2x=6-10$$

Subtract 10 from 6 to get -4.

$$-2x=-4$$

Divide both sides by -2.

$$x=\frac{-4}{-2}$$

Divide -4 by -2 to get 2.

$$x=2$$