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

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

Step 1

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

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

Step 2

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

Subtract $\frac{3 x}{2}$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Subtract $3 x$ from $x \cdot 2$ .

Reorder $x$ and $2$ .

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

Subtract $3 x$ from $2 \cdot x$ .

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

Move the negative in front of the fraction.

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

Step 3

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

Subtract $3$ from both sides of the equation.

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

Subtract $3$ from $2$ .

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

Step 4

Multiply both sides of the equation by $- 2$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - x = - 2 \cdot - 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot - 1$

Multiply $x$ by $1$ .

$x = - 2 \cdot - 1$

Simplify the right side.

Multiply $- 2$ by $- 1$ .

$x = 2$

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

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