Finite Math Examples

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

Step 1

Multiply both sides by $3$ .

$\frac{2 x - 6}{3} \cdot 3 = 1 \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{2 x - 6}{3} \cdot 3$ .

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Step 2.1.1.1

Factor $2$ out of $2 x - 6$ .

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Step 2.1.1.1.1

Factor $2$ out of $2 x$ .

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

Step 2.1.1.1.2

Factor $2$ out of $- 6$ .

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

Step 2.1.1.1.3

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

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

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

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Cancel the common factor.

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

Step 2.1.1.2.2

Rewrite the expression.

$2 (x - 3) = 1 \cdot 3$

$2 (x - 3) = 1 \cdot 3$

Step 2.1.1.3

Apply the distributive property.

$2 x + 2 \cdot - 3 = 1 \cdot 3$

Step 2.1.1.4

Multiply $2$ by $- 3$ .

$2 x - 6 = 1 \cdot 3$

$2 x - 6 = 1 \cdot 3$

$2 x - 6 = 1 \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $3$ by $1$ .

$2 x - 6 = 3$

$2 x - 6 = 3$

$2 x - 6 = 3$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Add $6$ to both sides of the equation.

$2 x = 3 + 6$

Step 3.1.2

Add $3$ and $6$ .

$2 x = 9$

$2 x = 9$

Step 3.2

Divide each term in $2 x = 9$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 x = 9$ by $2$ .

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

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.1.2

Divide $x$ by $1$ .

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

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

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

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 4.5$

Mixed Number Form:

$x = 4 \frac{1}{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$