Algebra Examples

$\frac{2}{5} (2 x - 3) > 6$

Step 1

Solve $x > 9$ .

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Step 1.1

Multiply each term in $\frac{2}{5} (2 x - 3) > 6$ by $\frac{5}{2}$ to eliminate the fractions.

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Step 1.1.1

Multiply each term in $\frac{2}{5} (2 x - 3) > 6$ by $\frac{5}{2}$ .

$\frac{2}{5} (2 x - 3) \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2

Simplify the left side.

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Step 1.1.2.1

Apply the distributive property.

$(\frac{2}{5} (2 x) + \frac{2}{5} \cdot - 3) \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.2

Multiply $\frac{2}{5} (2 x)$ .

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Step 1.1.2.2.1

Combine $2$ and $\frac{2}{5}$ .

$(\frac{2 \cdot 2}{5} x + \frac{2}{5} \cdot - 3) \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.2.2

Multiply $2$ by $2$ .

$(\frac{4}{5} x + \frac{2}{5} \cdot - 3) \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.2.3

Combine $\frac{4}{5}$ and $x$ .

$(\frac{4 x}{5} + \frac{2}{5} \cdot - 3) \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.3

Multiply $\frac{2}{5} \cdot - 3$ .

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Step 1.1.2.3.1

Combine $\frac{2}{5}$ and $- 3$ .

$(\frac{4 x}{5} + \frac{2 \cdot - 3}{5}) \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.3.2

Multiply $2$ by $- 3$ .

$(\frac{4 x}{5} + \frac{- 6}{5}) \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.4

Move the negative in front of the fraction.

$(\frac{4 x}{5} - \frac{6}{5}) \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.5

Apply the distributive property.

$\frac{4 x}{5} \cdot \frac{5}{2} - \frac{6}{5} \cdot \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.6

Cancel the common factor of $2$ .

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Step 1.1.2.6.1

Factor $2$ out of $4 x$ .

$\frac{2 (2 x)}{5} \cdot \frac{5}{2} - \frac{6}{5} \cdot \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.6.2

Cancel the common factor.

$\frac{2 (2 x)}{5} \cdot \frac{5}{2} - \frac{6}{5} \cdot \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.6.3

Rewrite the expression.

$\frac{2 x}{5} \cdot 5 - \frac{6}{5} \cdot \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.7

Cancel the common factor of $5$ .

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Step 1.1.2.7.1

Cancel the common factor.

$\frac{2 x}{5} \cdot 5 - \frac{6}{5} \cdot \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.7.2

Rewrite the expression.

$2 x - \frac{6}{5} \cdot \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.8

Cancel the common factor of $2$ .

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Step 1.1.2.8.1

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$2 x + \frac{- 6}{5} \cdot \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.8.2

Factor $2$ out of $- 6$ .

$2 x + \frac{2 (- 3)}{5} \cdot \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.8.3

Cancel the common factor.

$2 x + \frac{2 \cdot - 3}{5} \cdot \frac{5}{2} > 6 (\frac{5}{2})$

Step 1.1.2.8.4

Rewrite the expression.

$2 x + \frac{- 3}{5} \cdot 5 > 6 (\frac{5}{2})$

Step 1.1.2.9

Cancel the common factor of $5$ .

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Step 1.1.2.9.1

Cancel the common factor.

$2 x + \frac{- 3}{5} \cdot 5 > 6 (\frac{5}{2})$

Step 1.1.2.9.2

Rewrite the expression.

$2 x - 3 > 6 (\frac{5}{2})$

Step 1.1.3

Simplify the right side.

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Step 1.1.3.1

Cancel the common factor of $2$ .

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Step 1.1.3.1.1

Factor $2$ out of $6$ .

$2 x - 3 > 2 (3) \frac{5}{2}$

Step 1.1.3.1.2

Cancel the common factor.

$2 x - 3 > 2 \cdot 3 \frac{5}{2}$

Step 1.1.3.1.3

Rewrite the expression.

$2 x - 3 > 3 \cdot 5$

Step 1.1.3.2

Multiply $3$ by $5$ .

$2 x - 3 > 15$

Step 1.2

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

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Step 1.2.1

Add $3$ to both sides of the inequality.

$2 x > 15 + 3$

Step 1.2.2

Add $15$ and $3$ .

$2 x > 18$

Step 1.3

Divide each term in $2 x > 18$ by $2$ and simplify.

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Step 1.3.1

Divide each term in $2 x > 18$ by $2$ .

$\frac{2 x}{2} > \frac{18}{2}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $2$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} > \frac{18}{2}$

Step 1.3.2.1.2

Divide $x$ by $1$ .

$x > \frac{18}{2}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Divide $18$ by $2$ .

$x > 9$

Step 2

Use the inequality $x > 9$ to build the set notation.

${x | x > 9}$

Step 3