Algebra Examples

$x < 2 x - (- 8 x + \frac{6}{5})$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$2 x - (- 8 x + \frac{6}{5}) > x$

Step 2

Simplify $2 x - (- 8 x + \frac{6}{5})$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$2 x - (- 8 x) - \frac{6}{5} > x$

Step 2.1.2

Multiply $- 8$ by $- 1$ .

$2 x + 8 x - \frac{6}{5} > x$

Step 2.2

Add $2 x$ and $8 x$ .

$10 x - \frac{6}{5} > x$

Step 3

Move all terms containing $x$ to the left side of the inequality.

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Step 3.1

Subtract $x$ from both sides of the inequality.

$10 x - \frac{6}{5} - x > 0$

Step 3.2

Subtract $x$ from $10 x$ .

$9 x - \frac{6}{5} > 0$

Step 4

Add $\frac{6}{5}$ to both sides of the inequality.

$9 x > \frac{6}{5}$

Step 5

Divide each term in $9 x > \frac{6}{5}$ by $9$ and simplify.

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Step 5.1

Divide each term in $9 x > \frac{6}{5}$ by $9$ .

$\frac{9 x}{9} > \frac{\frac{6}{5}}{9}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $9$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{9 x}{9} > \frac{\frac{6}{5}}{9}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x > \frac{\frac{6}{5}}{9}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$x > \frac{6}{5} \cdot \frac{1}{9}$

Step 5.3.2

Cancel the common factor of $3$ .

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Step 5.3.2.1

Factor $3$ out of $6$ .

$x > \frac{3 (2)}{5} \cdot \frac{1}{9}$

Step 5.3.2.2

Factor $3$ out of $9$ .

$x > \frac{3 \cdot 2}{5} \cdot \frac{1}{3 \cdot 3}$

Step 5.3.2.3

Cancel the common factor.

$x > \frac{3 \cdot 2}{5} \cdot \frac{1}{3 \cdot 3}$

Step 5.3.2.4

Rewrite the expression.

$x > \frac{2}{5} \cdot \frac{1}{3}$

Step 5.3.3

Multiply $\frac{2}{5}$ by $\frac{1}{3}$ .

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

Step 5.3.4

Multiply $5$ by $3$ .

$x > \frac{2}{15}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{2}{15}$

Interval Notation:

$(\frac{2}{15}, \infty)$