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

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

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Combine \frac{1}{2}x and 3x to get \frac{7}{2}x.

$$\frac{7}{2}x+2-x+\frac{1}{2}\left(-2-3x\right)=1$$

Combine \frac{7}{2}x and -x to get \frac{5}{2}x.

$$\frac{5}{2}x+2+\frac{1}{2}\left(-2-3x\right)=1$$

Use the distributive property to multiply \frac{1}{2} by -2-3x.

$$\frac{5}{2}x+2+\frac{1}{2}\left(-2\right)+\frac{1}{2}\left(-3\right)x=1$$

Multiply \frac{1}{2} and -2 to get \frac{-2}{2}.

$$\frac{5}{2}x+2+\frac{-2}{2}+\frac{1}{2}\left(-3\right)x=1$$

Divide -2 by 2 to get -1.

$$\frac{5}{2}x+2-1+\frac{1}{2}\left(-3\right)x=1$$

Multiply \frac{1}{2} and -3 to get \frac{-3}{2}.

$$\frac{5}{2}x+2-1+\frac{-3}{2}x=1$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$\frac{5}{2}x+2-1-\frac{3}{2}x=1$$

Subtract 1 from 2 to get 1.

$$\frac{5}{2}x+1-\frac{3}{2}x=1$$

Combine \frac{5}{2}x and -\frac{3}{2}x to get x.

$$x+1=1$$

Subtract 1 from both sides.

$$x=1-1$$

Subtract 1 from 1 to get 0.

$$x=0$$