Finite Math Examples

$\frac{x + 7}{16} = \frac{1}{8} + \frac{x - 6}{3}$

Step 1

Simplify $\frac{1}{8} + \frac{x - 6}{3}$ .

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Step 1.1

To write $\frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x + 7}{16} = \frac{1}{8} \cdot \frac{3}{3} + \frac{x - 6}{3}$

Step 1.2

To write $\frac{x - 6}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{x + 7}{16} = \frac{1}{8} \cdot \frac{3}{3} + \frac{x - 6}{3} \cdot \frac{8}{8}$

Step 1.3

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{8}$ by $\frac{3}{3}$ .

$\frac{x + 7}{16} = \frac{3}{8 \cdot 3} + \frac{x - 6}{3} \cdot \frac{8}{8}$

Step 1.3.2

Multiply $8$ by $3$ .

$\frac{x + 7}{16} = \frac{3}{24} + \frac{x - 6}{3} \cdot \frac{8}{8}$

Step 1.3.3

Multiply $\frac{x - 6}{3}$ by $\frac{8}{8}$ .

$\frac{x + 7}{16} = \frac{3}{24} + \frac{(x - 6) \cdot 8}{3 \cdot 8}$

Step 1.3.4

Multiply $3$ by $8$ .

$\frac{x + 7}{16} = \frac{3}{24} + \frac{(x - 6) \cdot 8}{24}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x + 7}{16} = \frac{3 + (x - 6) \cdot 8}{24}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{x + 7}{16} = \frac{3 + x \cdot 8 - 6 \cdot 8}{24}$

Step 1.5.2

Move $8$ to the left of $x$ .

$\frac{x + 7}{16} = \frac{3 + 8 \cdot x - 6 \cdot 8}{24}$

Step 1.5.3

Multiply $- 6$ by $8$ .

$\frac{x + 7}{16} = \frac{3 + 8 \cdot x - 48}{24}$

Step 1.5.4

Subtract $48$ from $3$ .

$\frac{x + 7}{16} = \frac{8 x - 45}{24}$

Step 2

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

$x \approx 8.53846154$

Step 3