Trigonometry Examples

$\frac{1}{4} a + \frac{1}{4} \cdot (a - 8) = 9$

Step 1

Simplify $\frac{1}{4} a + \frac{1}{4} \cdot (a - 8)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{4}$ and $a$ .

$\frac{a}{4} + \frac{1}{4} \cdot (a - 8) = 9$

Step 1.1.2

Apply the distributive property.

$\frac{a}{4} + \frac{1}{4} a + \frac{1}{4} \cdot - 8 = 9$

Step 1.1.3

Combine $\frac{1}{4}$ and $a$ .

$\frac{a}{4} + \frac{a}{4} + \frac{1}{4} \cdot - 8 = 9$

Step 1.1.4

Cancel the common factor of $4$ .

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Step 1.1.4.1

Factor $4$ out of $- 8$ .

$\frac{a}{4} + \frac{a}{4} + \frac{1}{4} \cdot (4 (- 2)) = 9$

Step 1.1.4.2

Cancel the common factor.

$\frac{a}{4} + \frac{a}{4} + \frac{1}{4} \cdot (4 \cdot - 2) = 9$

Step 1.1.4.3

Rewrite the expression.

$\frac{a}{4} + \frac{a}{4} - 2 = 9$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$- 2 + \frac{a + a}{4} = 9$

Step 1.2.2

Add $a$ and $a$ .

$- 2 + \frac{2 a}{4} = 9$

Step 1.2.3

Cancel the common factor of $2$ and $4$ .

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Step 1.2.3.1

Factor $2$ out of $2 a$ .

$- 2 + \frac{2 (a)}{4} = 9$

Step 1.2.3.2

Cancel the common factors.

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Step 1.2.3.2.1

Factor $2$ out of $4$ .

$- 2 + \frac{2 a}{2 \cdot 2} = 9$

Step 1.2.3.2.2

Cancel the common factor.

$- 2 + \frac{2 a}{2 \cdot 2} = 9$

Step 1.2.3.2.3

Rewrite the expression.

$- 2 + \frac{a}{2} = 9$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$a \approx 22$

Step 3