Algebra Examples

$- x - 2 (- \frac{1}{2} x - \frac{4}{5}) > \frac{7}{5} - 3 x$

Step 1

Simplify $- x - 2 (- \frac{1}{2} x - \frac{4}{5})$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $x$ and $\frac{1}{2}$ .

$- x - 2 (- \frac{x}{2} - \frac{4}{5}) > \frac{7}{5} - 3 x$

Step 1.1.2

Apply the distributive property.

$- x - 2 (- \frac{x}{2}) - 2 (- \frac{4}{5}) > \frac{7}{5} - 3 x$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$- x - 2 \frac{- x}{2} - 2 (- \frac{4}{5}) > \frac{7}{5} - 3 x$

Step 1.1.3.2

Factor $2$ out of $- 2$ .

$- x + 2 (- 1) \frac{- x}{2} - 2 (- \frac{4}{5}) > \frac{7}{5} - 3 x$

Step 1.1.3.3

Cancel the common factor.

$- x + 2 \cdot - 1 \frac{- x}{2} - 2 (- \frac{4}{5}) > \frac{7}{5} - 3 x$

Step 1.1.3.4

Rewrite the expression.

$- x - 1 (- x) - 2 (- \frac{4}{5}) > \frac{7}{5} - 3 x$

Step 1.1.4

Multiply $- 1$ by $- 1$ .

$- x + 1 x - 2 (- \frac{4}{5}) > \frac{7}{5} - 3 x$

Step 1.1.5

Multiply $x$ by $1$ .

$- x + x - 2 (- \frac{4}{5}) > \frac{7}{5} - 3 x$

Step 1.1.6

Multiply $- 2 (- \frac{4}{5})$ .

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Step 1.1.6.1

Multiply $- 1$ by $- 2$ .

$- x + x + 2 (\frac{4}{5}) > \frac{7}{5} - 3 x$

Step 1.1.6.2

Combine $2$ and $\frac{4}{5}$ .

$- x + x + \frac{2 \cdot 4}{5} > \frac{7}{5} - 3 x$

Step 1.1.6.3

Multiply $2$ by $4$ .

$- x + x + \frac{8}{5} > \frac{7}{5} - 3 x$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $- x$ and $x$ .

$0 + \frac{8}{5} > \frac{7}{5} - 3 x$

Step 1.2.2

Add $0$ and $\frac{8}{5}$ .

$\frac{8}{5} > \frac{7}{5} - 3 x$

Step 2

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

$\frac{7}{5} - 3 x < \frac{8}{5}$

Step 3

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

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Step 3.1

Subtract $\frac{7}{5}$ from both sides of the inequality.

$- 3 x < \frac{8}{5} - \frac{7}{5}$

Step 3.2

Combine the numerators over the common denominator.

$- 3 x < \frac{8 - 7}{5}$

Step 3.3

Subtract $7$ from $8$ .

$- 3 x < \frac{1}{5}$

Step 4

Divide each term in $- 3 x < \frac{1}{5}$ by $- 3$ and simplify.

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Step 4.1

Divide each term in $- 3 x < \frac{1}{5}$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 3$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 4.3.2

Move the negative in front of the fraction.

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

Step 4.3.3

Multiply $\frac{1}{5} (- \frac{1}{3})$ .

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Step 4.3.3.1

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

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

Step 4.3.3.2

Multiply $5$ by $3$ .

$x > - \frac{1}{15}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{1}{15}$

Interval Notation:

$(- \frac{1}{15}, \infty)$