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

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

Solve for x

$$x = -\frac{10}{3} = -3\frac{1}{3} \approx -3.333333333$$

Steps for Solving Linear Equation

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

$$3\left(3x+1\right)+4=3\left(2x-1\right)$$

Use the distributive property to multiply 3 by 3x+1.

$$9x+3+4=3\left(2x-1\right)$$

Add 3 and 4 to get 7.

$$9x+7=3\left(2x-1\right)$$

Use the distributive property to multiply 3 by 2x-1.

$$9x+7=6x-3$$

Subtract 6x from both sides.

$$9x+7-6x=-3$$

Combine 9x and -6x to get 3x.

$$3x+7=-3$$

Subtract 7 from both sides.

$$3x=-3-7$$

Subtract 7 from -3 to get -10.

$$3x=-10$$

Divide both sides by 3.

$$x=\frac{-10}{3}$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$x=-\frac{10}{3}$$