Algebra Examples

$\frac{2}{3} + \frac{x}{5} = 6$

Step 1

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

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Step 1.1

Subtract $\frac{2}{3}$ from both sides of the equation.

$\frac{x}{5} = 6 - \frac{2}{3}$

Step 1.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{5} = 6 \cdot \frac{3}{3} - \frac{2}{3}$

Step 1.3

Combine $6$ and $\frac{3}{3}$ .

$\frac{x}{5} = \frac{6 \cdot 3}{3} - \frac{2}{3}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x}{5} = \frac{6 \cdot 3 - 2}{3}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $6$ by $3$ .

$\frac{x}{5} = \frac{18 - 2}{3}$

Step 1.5.2

Subtract $2$ from $18$ .

$\frac{x}{5} = \frac{16}{3}$

Step 2

Multiply both sides of the equation by $5$ .

$5 \frac{x}{5} = 5 (\frac{16}{3})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $5$ .

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Step 3.1.1.1

Cancel the common factor.

$5 \frac{x}{5} = 5 (\frac{16}{3})$

Step 3.1.1.2

Rewrite the expression.

$x = 5 (\frac{16}{3})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $5 (\frac{16}{3})$ .

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Step 3.2.1.1

Combine $5$ and $\frac{16}{3}$ .

$x = \frac{5 \cdot 16}{3}$

Step 3.2.1.2

Multiply $5$ by $16$ .

$x = \frac{80}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{80}{3}$

Decimal Form:

$x = 26.\overline{6}$

Mixed Number Form:

$x = 26 \frac{2}{3}$