Solve x-32x+1/2=-3left(-3x+9/3-2+xright)-x2/frac{2{2}}

$$x-3 \frac{ 2x+1 }{ 2 } = -3 \left( - \frac{ 3x+9 }{ 3 } -2+x \right) - \frac{ x2 }{ \frac{ 2 }{ 2 } }$$

Solve for x

$$x=\frac{x_{2}}{2}-\frac{33}{4}$$

Steps for Solving Linear Equation

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

$$6x-9\left(2x+1\right)=-18\left(-\frac{3x+9}{3}-2+x\right)-6x_{2}$$

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

$$6x-18x-9=-18\left(-\frac{3x+9}{3}-2+x\right)-6x_{2}$$

Combine 6x and -18x to get -12x.

$$-12x-9=-18\left(-\frac{3x+9}{3}-2+x\right)-6x_{2}$$

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

$$-12x-9=-18\left(-\left(3+x\right)-2+x\right)-6x_{2}$$

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

$$-12x-9=-18\left(-3-x-2+x\right)-6x_{2}$$

Subtract 2 from -3 to get -5.

$$-12x-9=-18\left(-5-x+x\right)-6x_{2}$$

Combine -x and x to get 0.

$$-12x-9=-18\left(-5\right)-6x_{2}$$

Multiply -18 and -5 to get 90.

$$-12x-9=90-6x_{2}$$

Add 9 to both sides.

$$-12x=90-6x_{2}+9$$

Add 90 and 9 to get 99.

$$-12x=99-6x_{2}$$

Divide both sides by -12.

$$\frac{-12x}{-12}=\frac{99-6x_{2}}{-12}$$

Dividing by -12 undoes the multiplication by -12.

$$x=\frac{99-6x_{2}}{-12}$$

Divide 99-6x_{2} by -12.

$$x=\frac{x_{2}}{2}-\frac{33}{4}$$

Solve for x_2

$$x_{2}=2x+\frac{33}{2}$$

Steps for Solving Linear Equation

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

$$6x-9\left(2x+1\right)=-18\left(-\frac{3x+9}{3}-2+x\right)-6x_{2}$$

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

$$6x-18x-9=-18\left(-\frac{3x+9}{3}-2+x\right)-6x_{2}$$

Combine 6x and -18x to get -12x.

$$-12x-9=-18\left(-\frac{3x+9}{3}-2+x\right)-6x_{2}$$

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

$$-12x-9=-18\left(-\left(3+x\right)-2+x\right)-6x_{2}$$

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

$$-12x-9=-18\left(-3-x-2+x\right)-6x_{2}$$

Subtract 2 from -3 to get -5.

$$-12x-9=-18\left(-5-x+x\right)-6x_{2}$$

Combine -x and x to get 0.

$$-12x-9=-18\left(-5\right)-6x_{2}$$

Multiply -18 and -5 to get 90.

$$-12x-9=90-6x_{2}$$

Swap sides so that all variable terms are on the left hand side.

$$90-6x_{2}=-12x-9$$

Subtract 90 from both sides.

$$-6x_{2}=-12x-9-90$$

Subtract 90 from -9 to get -99.

$$-6x_{2}=-12x-99$$

Divide both sides by -6.

$$\frac{-6x_{2}}{-6}=\frac{-12x-99}{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$x_{2}=\frac{-12x-99}{-6}$$

Divide -12x-99 by -6.

$$x_{2}=2x+\frac{33}{2}$$