Algebra Examples

$6 (x - 2) = 4$

Step 1

Divide each term in $6 (x - 2) = 4$ by $6$ and simplify.

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Step 1.1

Divide each term in $6 (x - 2) = 4$ by $6$ .

$\frac{6 (x - 2)}{6} = \frac{4}{6}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $6$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{6 (x - 2)}{6} = \frac{4}{6}$

Step 1.2.1.2

Divide $x - 2$ by $1$ .

$x - 2 = \frac{4}{6}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Cancel the common factor of $4$ and $6$ .

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Step 1.3.1.1

Factor $2$ out of $4$ .

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

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $2$ out of $6$ .

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

Step 1.3.1.2.2

Cancel the common factor.

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

Step 1.3.1.2.3

Rewrite the expression.

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

Step 2

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

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Step 2.1

Add $2$ to both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $3$ .

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

Step 2.5.2

Add $2$ and $6$ .

$x = \frac{8}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{8}{3}$

Decimal Form:

$x = 2.\overline{6}$

Mixed Number Form:

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