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

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

Step 1

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

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

Step 2

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

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

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

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x + 3 x \cdot 2$ .

Raise $x$ to the power of $1$ .

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

Factor $x$ out of $x^{1}$ .

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

Factor $x$ out of $3 x \cdot 2$ .

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

Factor $x$ out of $x \cdot 1 + x (3 \cdot 2)$ .

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

Multiply $3$ by $2$ .

$\frac{x (1 + 6)}{2} - 3 = \frac{3}{2}$

Add $1$ and $6$ .

$\frac{x \cdot 7}{2} - 3 = \frac{3}{2}$

Move $7$ to the left of $x$ .

$\frac{7 x}{2} - 3 = \frac{3}{2}$

Step 3

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

Add $3$ to both sides of the equation.

$\frac{7 x}{2} = \frac{3}{2} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 x}{2} = \frac{3}{2} + 3 \cdot \frac{2}{2}$

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

$\frac{7 x}{2} = \frac{3}{2} + \frac{3 \cdot 2}{2}$

Combine the numerators over the common denominator.

$\frac{7 x}{2} = \frac{3 + 3 \cdot 2}{2}$

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{7 x}{2} = \frac{3 + 6}{2}$

Add $3$ and $6$ .

$\frac{7 x}{2} = \frac{9}{2}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$7 x = 9$

Step 5

Divide each term in $7 x = 9$ by $7$ and simplify.

Divide each term in $7 x = 9$ by $7$ .

$\frac{7 x}{7} = \frac{9}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{9}{7}$

Divide $x$ by $1$ .

$x = \frac{9}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{7}$

Decimal Form:

$x = 1.\overline{285714}$

Mixed Number Form:

$x = 1 \frac{2}{7}$

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

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