Finite Math Examples

$\frac{x + 1}{8} = \frac{7}{4} + \frac{x - 2}{3}$

Step 1

Simplify $\frac{7}{4} + \frac{x - 2}{3}$ .

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Step 1.1

To write $\frac{7}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x + 1}{8} = \frac{7}{4} \cdot \frac{3}{3} + \frac{x - 2}{3}$

Step 1.2

To write $\frac{x - 2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x + 1}{8} = \frac{7}{4} \cdot \frac{3}{3} + \frac{x - 2}{3} \cdot \frac{4}{4}$

Step 1.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{7}{4}$ by $\frac{3}{3}$ .

$\frac{x + 1}{8} = \frac{7 \cdot 3}{4 \cdot 3} + \frac{x - 2}{3} \cdot \frac{4}{4}$

Step 1.3.2

Multiply $4$ by $3$ .

$\frac{x + 1}{8} = \frac{7 \cdot 3}{12} + \frac{x - 2}{3} \cdot \frac{4}{4}$

Step 1.3.3

Multiply $\frac{x - 2}{3}$ by $\frac{4}{4}$ .

$\frac{x + 1}{8} = \frac{7 \cdot 3}{12} + \frac{(x - 2) \cdot 4}{3 \cdot 4}$

Step 1.3.4

Multiply $3$ by $4$ .

$\frac{x + 1}{8} = \frac{7 \cdot 3}{12} + \frac{(x - 2) \cdot 4}{12}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x + 1}{8} = \frac{7 \cdot 3 + (x - 2) \cdot 4}{12}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $7$ by $3$ .

$\frac{x + 1}{8} = \frac{21 + (x - 2) \cdot 4}{12}$

Step 1.5.2

Apply the distributive property.

$\frac{x + 1}{8} = \frac{21 + x \cdot 4 - 2 \cdot 4}{12}$

Step 1.5.3

Move $4$ to the left of $x$ .

$\frac{x + 1}{8} = \frac{21 + 4 \cdot x - 2 \cdot 4}{12}$

Step 1.5.4

Multiply $- 2$ by $4$ .

$\frac{x + 1}{8} = \frac{21 + 4 \cdot x - 8}{12}$

Step 1.5.5

Subtract $8$ from $21$ .

$\frac{x + 1}{8} = \frac{4 x + 13}{12}$

Step 2

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

$x = - \frac{23}{5}$

Step 3