Pre-Algebra Examples

$\frac{8 t + 1}{6} = \frac{t + 8}{12} + \frac{t - 6}{6}$

Step 1

Simplify $\frac{t + 8}{12} + \frac{t - 6}{6}$ .

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Step 1.1

To write $\frac{t - 6}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{8 t + 1}{6} = \frac{t + 8}{12} + \frac{t - 6}{6} \cdot \frac{2}{2}$

Step 1.2

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

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Step 1.2.1

Multiply $\frac{t - 6}{6}$ by $\frac{2}{2}$ .

$\frac{8 t + 1}{6} = \frac{t + 8}{12} + \frac{(t - 6) \cdot 2}{6 \cdot 2}$

Step 1.2.2

Multiply $6$ by $2$ .

$\frac{8 t + 1}{6} = \frac{t + 8}{12} + \frac{(t - 6) \cdot 2}{12}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{8 t + 1}{6} = \frac{t + 8 + (t - 6) \cdot 2}{12}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Apply the distributive property.

$\frac{8 t + 1}{6} = \frac{t + 8 + t \cdot 2 - 6 \cdot 2}{12}$

Step 1.4.2

Move $2$ to the left of $t$ .

$\frac{8 t + 1}{6} = \frac{t + 8 + 2 \cdot t - 6 \cdot 2}{12}$

Step 1.4.3

Multiply $- 6$ by $2$ .

$\frac{8 t + 1}{6} = \frac{t + 8 + 2 \cdot t - 12}{12}$

Step 1.4.4

Add $t$ and $2 t$ .

$\frac{8 t + 1}{6} = \frac{3 t + 8 - 12}{12}$

Step 1.4.5

Subtract $12$ from $8$ .

$\frac{8 t + 1}{6} = \frac{3 t - 4}{12}$

Step 2

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

$t \approx - 0.46153846$

Step 3