Solve for x 3/2x+2=1/2-1/2x

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

Step 1

Combine $\frac{3}{2}$ and $x$ .

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

Step 2

Combine $x$ and $\frac{1}{2}$ .

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

Step 3

Move all terms containing $x$ to the left side of the equation.

Add $\frac{x}{2}$ to both sides of the equation.

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

Combine the numerators over the common denominator.

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

Add $3 x$ and $x$ .

$2 + \frac{4 x}{2} = \frac{1}{2}$

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 x$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2 + \frac{2 x}{1} = \frac{1}{2}$

Divide $2 x$ by $1$ .

$2 + 2 x = \frac{1}{2}$

Step 4

Move all terms not containing $x$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$2 x = \frac{1}{2} - 2$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 x = \frac{1}{2} - 2 \cdot \frac{2}{2}$

Combine $- 2$ and $\frac{2}{2}$ .

$2 x = \frac{1}{2} + \frac{- 2 \cdot 2}{2}$

Combine the numerators over the common denominator.

$2 x = \frac{1 - 2 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 2$ by $2$ .

$2 x = \frac{1 - 4}{2}$

Subtract $4$ from $1$ .

$2 x = \frac{- 3}{2}$

Move the negative in front of the fraction.

$2 x = - \frac{3}{2}$

Step 5

Divide each term in $2 x = - \frac{3}{2}$ by $2$ and simplify.

Divide each term in $2 x = - \frac{3}{2}$ by $2$ .

$\frac{2 x}{2} = \frac{- \frac{3}{2}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- \frac{3}{2}}{2}$

Divide $x$ by $1$ .

$x = \frac{- \frac{3}{2}}{2}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{3}{2} \cdot \frac{1}{2}$

Multiply $- \frac{3}{2} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{3}{2}$ .

$x = - \frac{3}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = - \frac{3}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{4}$

Decimal Form:

$x = - 0.75$

Solve for x 3/2x+2=1/2-1/2x

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