Pre-Algebra Examples

$8 r - \frac{r}{6} > \frac{1}{6} - 8$

Step 1

Simplify $8 r - \frac{r}{6}$ .

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Step 1.1

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

$8 r \cdot \frac{6}{6} - \frac{r}{6} > \frac{1}{6} - 8$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $8 r$ and $\frac{6}{6}$ .

$\frac{8 r \cdot 6}{6} - \frac{r}{6} > \frac{1}{6} - 8$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{8 r \cdot 6 - r}{6} > \frac{1}{6} - 8$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Factor $r$ out of $8 r \cdot 6 - r$ .

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Step 1.3.1.1

Factor $r$ out of $8 r \cdot 6$ .

$\frac{r (8 \cdot 6) - r}{6} > \frac{1}{6} - 8$

Step 1.3.1.2

Factor $r$ out of $- r$ .

$\frac{r (8 \cdot 6) + r \cdot - 1}{6} > \frac{1}{6} - 8$

Step 1.3.1.3

Factor $r$ out of $r (8 \cdot 6) + r \cdot - 1$ .

$\frac{r (8 \cdot 6 - 1)}{6} > \frac{1}{6} - 8$

Step 1.3.2

Multiply $8$ by $6$ .

$\frac{r (48 - 1)}{6} > \frac{1}{6} - 8$

Step 1.3.3

Subtract $1$ from $48$ .

$\frac{r \cdot 47}{6} > \frac{1}{6} - 8$

Step 1.4

Move $47$ to the left of $r$ .

$\frac{47 r}{6} > \frac{1}{6} - 8$

Step 2

Simplify $\frac{1}{6} - 8$ .

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Step 2.1

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

$\frac{47 r}{6} > \frac{1}{6} - 8 \cdot \frac{6}{6}$

Step 2.2

Combine $- 8$ and $\frac{6}{6}$ .

$\frac{47 r}{6} > \frac{1}{6} + \frac{- 8 \cdot 6}{6}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{47 r}{6} > \frac{1 - 8 \cdot 6}{6}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $- 8$ by $6$ .

$\frac{47 r}{6} > \frac{1 - 48}{6}$

Step 2.4.2

Subtract $48$ from $1$ .

$\frac{47 r}{6} > \frac{- 47}{6}$

Step 2.5

Move the negative in front of the fraction.

$\frac{47 r}{6} > - \frac{47}{6}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$47 r > - 47$

Step 4

Divide each term in $47 r > - 47$ by $47$ and simplify.

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Step 4.1

Divide each term in $47 r > - 47$ by $47$ .

$\frac{47 r}{47} > \frac{- 47}{47}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $47$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{47 r}{47} > \frac{- 47}{47}$

Step 4.2.1.2

Divide $r$ by $1$ .

$r > \frac{- 47}{47}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 47$ by $47$ .

$r > - 1$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$r > - 1$

Interval Notation:

$(- 1, \infty)$