Algebra Examples

$2 k + \frac{1}{3} > 1$

Step 1

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

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Step 1.1

Subtract $\frac{1}{3}$ from both sides of the inequality.

$2 k > 1 - \frac{1}{3}$

Step 1.2

Write $1$ as a fraction with a common denominator.

$2 k > \frac{3}{3} - \frac{1}{3}$

Step 1.3

Combine the numerators over the common denominator.

$2 k > \frac{3 - 1}{3}$

Step 1.4

Subtract $1$ from $3$ .

$2 k > \frac{2}{3}$

Step 2

Divide each term in $2 k > \frac{2}{3}$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 k > \frac{2}{3}$ by $2$ .

$\frac{2 k}{2} > \frac{\frac{2}{3}}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 k}{2} > \frac{\frac{2}{3}}{2}$

Step 2.2.1.2

Divide $k$ by $1$ .

$k > \frac{\frac{2}{3}}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$k > \frac{2}{3} \cdot \frac{1}{2}$

Step 2.3.2

Cancel the common factor of $2$ .

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Step 2.3.2.1

Cancel the common factor.

$k > \frac{2}{3} \cdot \frac{1}{2}$

Step 2.3.2.2

Rewrite the expression.

$k > \frac{1}{3}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$k > \frac{1}{3}$

Interval Notation:

$(\frac{1}{3}, \infty)$