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

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

Solve for x

$$x = -\frac{33}{2} = -16\frac{1}{2} = -16.5$$

Steps for Solving Linear Equation

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

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

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

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

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

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

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

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

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

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

Subtract 2 from -3 to get -5.

$$-12x-9=-18\left(-5-x+x\right)-6x$$

Combine -x and x to get 0.

$$-12x-9=-18\left(-5\right)-6x$$

Multiply -18 and -5 to get 90.

$$-12x-9=90-6x$$

Add 6x to both sides.

$$-12x-9+6x=90$$

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

$$-6x-9=90$$

Add 9 to both sides.

$$-6x=90+9$$

Add 90 and 9 to get 99.

$$-6x=99$$

Divide both sides by -6.

$$x=\frac{99}{-6}$$

Reduce the fraction \frac{99}{-6} to lowest terms by extracting and canceling out 3.

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