Solve 3(2x-1/2)=-3(-3x+9/3-2+x)-x/2

$$3 ( \frac { 2 x - 1 } { 2 } ) = - 3 ( - \frac { 3 x + 9 } { 3 } - 2 + x ) - \frac { x } { 2 }$$

Solve for x

$$x = \frac{33}{7} = 4\frac{5}{7} \approx 4.714285714$$

Steps for Solving Linear Equation

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

$$9\left(2x-1\right)=-18\left(-\frac{3x+9}{3}-2+x\right)-3x$$

Use the distributive property to multiply 9 by 2x-1.

$$18x-9=-18\left(-\frac{3x+9}{3}-2+x\right)-3x$$

Divide each term of 3x+9 by 3 to get 3+x.

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

To find the opposite of 3+x, find the opposite of each term.

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

Subtract 2 from -3 to get -5.

$$18x-9=-18\left(-5-x+x\right)-3x$$

Combine -x and x to get 0.

$$18x-9=-18\left(-5\right)-3x$$

Multiply -18 and -5 to get 90.

$$18x-9=90-3x$$

Add 3x to both sides.

$$18x-9+3x=90$$

Combine 18x and 3x to get 21x.

$$21x-9=90$$

Add 9 to both sides.

$$21x=90+9$$

Add 90 and 9 to get 99.

$$21x=99$$

Divide both sides by 21.

$$x=\frac{99}{21}$$

Reduce the fraction \frac{99}{21} to lowest terms by extracting and canceling out 3.

$$x=\frac{33}{7}$$