Trigonometry Examples

$x + \frac{3}{5} + \frac{x}{3} = 7$

Step 1

Simplify $x + \frac{3}{5} + \frac{x}{3}$ .

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Step 1.1

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

$x \cdot \frac{3}{3} + \frac{x}{3} + \frac{3}{5} = 7$

Step 1.2

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

$\frac{x \cdot 3}{3} + \frac{x}{3} + \frac{3}{5} = 7$

Step 1.3

Combine the numerators over the common denominator.

$\frac{x \cdot 3 + x}{3} + \frac{3}{5} = 7$

Step 1.4

Add $x \cdot 3$ and $x$ .

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Step 1.4.1

Reorder $x$ and $3$ .

$\frac{3 \cdot x + x}{3} + \frac{3}{5} = 7$

Step 1.4.2

Add $3 \cdot x$ and $x$ .

$\frac{4 \cdot x}{3} + \frac{3}{5} = 7$

$\frac{4 x}{3} + \frac{3}{5} = 7$

Step 2

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

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Step 2.1

Subtract $\frac{3}{5}$ from both sides of the equation.

$\frac{4 x}{3} = 7 - \frac{3}{5}$

Step 2.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4 x}{3} = 7 \cdot \frac{5}{5} - \frac{3}{5}$

Step 2.3

Combine $7$ and $\frac{5}{5}$ .

$\frac{4 x}{3} = \frac{7 \cdot 5}{5} - \frac{3}{5}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{4 x}{3} = \frac{7 \cdot 5 - 3}{5}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $7$ by $5$ .

$\frac{4 x}{3} = \frac{35 - 3}{5}$

Step 2.5.2

Subtract $3$ from $35$ .

$\frac{4 x}{3} = \frac{32}{5}$

Step 3

Multiply both sides of the equation by $\frac{3}{4}$ .

$\frac{3}{4} \cdot \frac{4 x}{3} = \frac{3}{4} \cdot \frac{32}{5}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{3}{4} \cdot \frac{4 x}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{3}{4} \cdot \frac{4 x}{3} = \frac{3}{4} \cdot \frac{32}{5}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 x) = \frac{3}{4} \cdot \frac{32}{5}$

Step 4.1.1.2

Cancel the common factor of $4$ .

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Step 4.1.1.2.1

Factor $4$ out of $4 x$ .

$\frac{1}{4} (4 (x)) = \frac{3}{4} \cdot \frac{32}{5}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 x) = \frac{3}{4} \cdot \frac{32}{5}$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{3}{4} \cdot \frac{32}{5}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{3}{4} \cdot \frac{32}{5}$ .

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Step 4.2.1.1

Cancel the common factor of $4$ .

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Step 4.2.1.1.1

Factor $4$ out of $32$ .

$x = \frac{3}{4} \cdot \frac{4 (8)}{5}$

Step 4.2.1.1.2

Cancel the common factor.

$x = \frac{3}{4} \cdot \frac{4 \cdot 8}{5}$

Step 4.2.1.1.3

Rewrite the expression.

$x = 3 (\frac{8}{5})$

Step 4.2.1.2

Combine $3$ and $\frac{8}{5}$ .

$x = \frac{3 \cdot 8}{5}$

Step 4.2.1.3

Multiply $3$ by $8$ .

$x = \frac{24}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{24}{5}$

Decimal Form:

$x = 4.8$

Mixed Number Form:

$x = 4 \frac{4}{5}$