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

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

Solve for x

$$x=7$$

Steps for Solving Linear Equation

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

$$3\left(3x-1\right)-18=6+2\times 2\left(x+2\right)$$

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

$$9x-3-18=6+2\times 2\left(x+2\right)$$

Subtract 18 from -3 to get -21.

$$9x-21=6+2\times 2\left(x+2\right)$$

Multiply 2 and 2 to get 4.

$$9x-21=6+4\left(x+2\right)$$

Use the distributive property to multiply 4 by x+2.

$$9x-21=6+4x+8$$

Add 6 and 8 to get 14.

$$9x-21=14+4x$$

Subtract 4x from both sides.

$$9x-21-4x=14$$

Combine 9x and -4x to get 5x.

$$5x-21=14$$

Add 21 to both sides.

$$5x=14+21$$

Add 14 and 21 to get 35.

$$5x=35$$

Divide both sides by 5.

$$x=\frac{35}{5}$$

Divide 35 by 5 to get 7.

$$x=7$$