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

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

Solve for x

$$x = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$18\left(x-1\right)+2\left(x+1\right)=9$$

Use the distributive property to multiply 18 by x-1.

$$18x-18+2\left(x+1\right)=9$$

Use the distributive property to multiply 2 by x+1.

$$18x-18+2x+2=9$$

Combine 18x and 2x to get 20x.

$$20x-18+2=9$$

Add -18 and 2 to get -16.

$$20x-16=9$$

Add 16 to both sides.

$$20x=9+16$$

Add 9 and 16 to get 25.

$$20x=25$$

Divide both sides by 20.

$$x=\frac{25}{20}$$

Reduce the fraction \frac{25}{20} to lowest terms by extracting and canceling out 5.

$$x=\frac{5}{4}$$