Pre-Algebra Examples

$- \frac{7}{11} k + 2 < \frac{2}{3}$

Step 1

Simplify each term.

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Step 1.1

Combine $k$ and $\frac{7}{11}$ .

$- \frac{k \cdot 7}{11} + 2 < \frac{2}{3}$

Step 1.2

Move $7$ to the left of $k$ .

$- \frac{7 k}{11} + 2 < \frac{2}{3}$

Step 2

Move all terms not containing $k$ to the right side of the inequality.

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Step 2.1

Subtract $2$ from both sides of the inequality.

$- \frac{7 k}{11} < \frac{2}{3} - 2$

Step 2.2

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

$- \frac{7 k}{11} < \frac{2}{3} - 2 \cdot \frac{3}{3}$

Step 2.3

Combine $- 2$ and $\frac{3}{3}$ .

$- \frac{7 k}{11} < \frac{2}{3} + \frac{- 2 \cdot 3}{3}$

Step 2.4

Combine the numerators over the common denominator.

$- \frac{7 k}{11} < \frac{2 - 2 \cdot 3}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 2$ by $3$ .

$- \frac{7 k}{11} < \frac{2 - 6}{3}$

Step 2.5.2

Subtract $6$ from $2$ .

$- \frac{7 k}{11} < \frac{- 4}{3}$

Step 2.6

Move the negative in front of the fraction.

$- \frac{7 k}{11} < - \frac{4}{3}$

Step 3

Divide each term in $- \frac{7 k}{11} < - \frac{4}{3}$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- \frac{7 k}{11} < - \frac{4}{3}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{7 k}{11}}{- 1} > \frac{- \frac{4}{3}}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{7 k}{11}}{1} > \frac{- \frac{4}{3}}{- 1}$

Step 3.2.2

Divide $\frac{7 k}{11}$ by $1$ .

$\frac{7 k}{11} > \frac{- \frac{4}{3}}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

$\frac{7 k}{11} > \frac{\frac{4}{3}}{1}$

Step 3.3.2

Divide $\frac{4}{3}$ by $1$ .

$\frac{7 k}{11} > \frac{4}{3}$

Step 4

Multiply both sides by $11$ .

$\frac{7 k}{11} \cdot 11 > \frac{4}{3} \cdot 11$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $11$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{7 k}{11} \cdot 11 > \frac{4}{3} \cdot 11$

Step 5.1.1.2

Rewrite the expression.

$7 k > \frac{4}{3} \cdot 11$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $\frac{4}{3} \cdot 11$ .

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Step 5.2.1.1

Combine $\frac{4}{3}$ and $11$ .

$7 k > \frac{4 \cdot 11}{3}$

Step 5.2.1.2

Multiply $4$ by $11$ .

$7 k > \frac{44}{3}$

Step 6

Divide each term in $7 k > \frac{44}{3}$ by $7$ and simplify.

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Step 6.1

Divide each term in $7 k > \frac{44}{3}$ by $7$ .

$\frac{7 k}{7} > \frac{\frac{44}{3}}{7}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $7$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{7 k}{7} > \frac{\frac{44}{3}}{7}$

Step 6.2.1.2

Divide $k$ by $1$ .

$k > \frac{\frac{44}{3}}{7}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Multiply the numerator by the reciprocal of the denominator.

$k > \frac{44}{3} \cdot \frac{1}{7}$

Step 6.3.2

Multiply $\frac{44}{3} \cdot \frac{1}{7}$ .

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Step 6.3.2.1

Multiply $\frac{44}{3}$ by $\frac{1}{7}$ .

$k > \frac{44}{3 \cdot 7}$

Step 6.3.2.2

Multiply $3$ by $7$ .

$k > \frac{44}{21}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$k > \frac{44}{21}$

Interval Notation:

$(\frac{44}{21}, \infty)$