Algebra Examples

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

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 2

Simplify $\frac{3}{2} x + 4 - x$ .

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Simplify terms.

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Step 2.3.1

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

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

Step 2.3.2

Combine the numerators over the common denominator.

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

Step 2.4

Simplify each term.

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Step 2.4.1

Simplify the numerator.

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Step 2.4.1.1

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

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Step 2.4.1.1.1

Factor $x$ out of $3 x$ .

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

Step 2.4.1.1.2

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

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

Step 2.4.1.1.3

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

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

Step 2.4.1.2

Multiply $- 1$ by $2$ .

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

Step 2.4.1.3

Subtract $2$ from $3$ .

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

Step 2.4.2

Multiply $x$ by $1$ .

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

Step 3

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

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

Step 4

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

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Step 4.1

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

$\frac{x}{2} + 4 + \frac{x}{2} = 3$

Step 4.2

Combine the numerators over the common denominator.

$4 + \frac{x + x}{2} = 3$

Step 4.3

Add $x$ and $x$ .

$4 + \frac{2 x}{2} = 3$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

$4 + \frac{2 x}{2} = 3$

Step 4.4.2

Divide $x$ by $1$ .

$4 + x = 3$

Step 5

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

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Step 5.1

Subtract $4$ from both sides of the equation.

$x = 3 - 4$

Step 5.2

Subtract $4$ from $3$ .

$x = - 1$