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

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

Step 1

Simplify $\frac{3 x}{2} + \frac{1}{2} x - x$ .

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

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

Combine the numerators over the common denominator.

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

Add $3 x$ and $x$ .

$- x + \frac{4 x}{2} = 1 - 3 (x - 3)$

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

Factor $2$ out of $4 x$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 x$ by $1$ .

$- x + 2 x = 1 - 3 (x - 3)$

Add $- x$ and $2 x$ .

$x = 1 - 3 (x - 3)$

Step 2

Simplify $1 - 3 (x - 3)$ .

Simplify each term.

Apply the distributive property.

$x = 1 - 3 x - 3 \cdot - 3$

Multiply $- 3$ by $- 3$ .

$x = 1 - 3 x + 9$

Add $1$ and $9$ .

$x = - 3 x + 10$

Step 3

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

Add $3 x$ to both sides of the equation.

$x + 3 x = 10$

Add $x$ and $3 x$ .

$4 x = 10$

Step 4

Divide each term in $4 x = 10$ by $4$ and simplify.

Divide each term in $4 x = 10$ by $4$ .

$\frac{4 x}{4} = \frac{10}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{10}{4}$

Divide $x$ by $1$ .

$x = \frac{10}{4}$

Simplify the right side.

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$x = \frac{2 (5)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 5}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot 5}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{5}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{2}$

Decimal Form:

$x = 2.5$

Mixed Number Form:

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

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

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