Finite Math Examples

$3 x - \frac{x}{2} = 0$

Step 1

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

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Step 1.1

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

$3 x \cdot \frac{2}{2} - \frac{x}{2} = 0$

Step 1.2

Simplify terms.

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Step 1.2.1

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

$\frac{3 x \cdot 2}{2} - \frac{x}{2} = 0$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{3 x \cdot 2 - x}{2} = 0$

Step 1.3

Simplify the numerator.

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Step 1.3.1

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

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Step 1.3.1.1

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

$\frac{x (3 \cdot 2) - x}{2} = 0$

Step 1.3.1.2

Factor $x$ out of $- x$ .

$\frac{x (3 \cdot 2) + x \cdot - 1}{2} = 0$

Step 1.3.1.3

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

$\frac{x (3 \cdot 2 - 1)}{2} = 0$

Step 1.3.2

Multiply $3$ by $2$ .

$\frac{x (6 - 1)}{2} = 0$

Step 1.3.3

Subtract $1$ from $6$ .

$\frac{x \cdot 5}{2} = 0$

Step 1.4

Move $5$ to the left of $x$ .

$\frac{5 x}{2} = 0$

Step 2

Set the numerator equal to zero.

$5 x = 0$

Step 3

Divide each term in $5 x = 0$ by $5$ and simplify.

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Step 3.1

Divide each term in $5 x = 0$ by $5$ .

$\frac{5 x}{5} = \frac{0}{5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{0}{5}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{5}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0$ by $5$ .

$x = 0$