Algebra Examples

$2 + 2 (2 x - \frac{6}{5}) > - 2 x - 1$

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 + 2 (2 x) + 2 (- \frac{6}{5}) > - 2 x - 1$

Step 1.1.2

Multiply $2$ by $2$ .

$2 + 4 x + 2 (- \frac{6}{5}) > - 2 x - 1$

Step 1.1.3

Multiply $2 (- \frac{6}{5})$ .

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Step 1.1.3.1

Multiply $- 1$ by $2$ .

$2 + 4 x - 2 (\frac{6}{5}) > - 2 x - 1$

Step 1.1.3.2

Combine $- 2$ and $\frac{6}{5}$ .

$2 + 4 x + \frac{- 2 \cdot 6}{5} > - 2 x - 1$

Step 1.1.3.3

Multiply $- 2$ by $6$ .

$2 + 4 x + \frac{- 12}{5} > - 2 x - 1$

Step 1.1.4

Move the negative in front of the fraction.

$2 + 4 x - \frac{12}{5} > - 2 x - 1$

Step 1.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$4 x + 2 \cdot \frac{5}{5} - \frac{12}{5} > - 2 x - 1$

Step 1.3

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

$4 x + \frac{2 \cdot 5}{5} - \frac{12}{5} > - 2 x - 1$

Step 1.4

Combine the numerators over the common denominator.

$4 x + \frac{2 \cdot 5 - 12}{5} > - 2 x - 1$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $2$ by $5$ .

$4 x + \frac{10 - 12}{5} > - 2 x - 1$

Step 1.5.2

Subtract $12$ from $10$ .

$4 x + \frac{- 2}{5} > - 2 x - 1$

Step 1.6

Move the negative in front of the fraction.

$4 x - \frac{2}{5} > - 2 x - 1$

Step 2

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

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Step 2.1

Add $2 x$ to both sides of the inequality.

$4 x - \frac{2}{5} + 2 x > - 1$

Step 2.2

Add $4 x$ and $2 x$ .

$6 x - \frac{2}{5} > - 1$

Step 3

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

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Step 3.1

Add $\frac{2}{5}$ to both sides of the inequality.

$6 x > - 1 + \frac{2}{5}$

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$6 x > - 1 \cdot \frac{5}{5} + \frac{2}{5}$

Step 3.3

Combine $- 1$ and $\frac{5}{5}$ .

$6 x > \frac{- 1 \cdot 5}{5} + \frac{2}{5}$

Step 3.4

Combine the numerators over the common denominator.

$6 x > \frac{- 1 \cdot 5 + 2}{5}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 1$ by $5$ .

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

Step 3.5.2

Add $- 5$ and $2$ .

$6 x > \frac{- 3}{5}$

Step 3.6

Move the negative in front of the fraction.

$6 x > - \frac{3}{5}$

Step 4

Divide each term in $6 x > - \frac{3}{5}$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 x > - \frac{3}{5}$ by $6$ .

$\frac{6 x}{6} > \frac{- \frac{3}{5}}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 x}{6} > \frac{- \frac{3}{5}}{6}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x > \frac{- \frac{3}{5}}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$x > - \frac{3}{5} \cdot \frac{1}{6}$

Step 4.3.2

Cancel the common factor of $3$ .

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Step 4.3.2.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$x > \frac{- 3}{5} \cdot \frac{1}{6}$

Step 4.3.2.2

Factor $3$ out of $- 3$ .

$x > \frac{3 (- 1)}{5} \cdot \frac{1}{6}$

Step 4.3.2.3

Factor $3$ out of $6$ .

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

Step 4.3.2.4

Cancel the common factor.

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

Step 4.3.2.5

Rewrite the expression.

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

Step 4.3.3

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

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

Step 4.3.4

Simplify the expression.

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Step 4.3.4.1

Multiply $5$ by $2$ .

$x > \frac{- 1}{10}$

Step 4.3.4.2

Move the negative in front of the fraction.

$x > - \frac{1}{10}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{1}{10}$

Interval Notation:

$(- \frac{1}{10}, \infty)$