Algebra Examples

$\frac{6}{7} > - 2 x - \frac{8}{7}$

Step 1

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

$- 2 x - \frac{8}{7} < \frac{6}{7}$

Step 2

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

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Step 2.1

Add $\frac{8}{7}$ to both sides of the inequality.

$- 2 x < \frac{6}{7} + \frac{8}{7}$

Step 2.2

Combine the numerators over the common denominator.

$- 2 x < \frac{6 + 8}{7}$

Step 2.3

Add $6$ and $8$ .

$- 2 x < \frac{14}{7}$

Step 2.4

Divide $14$ by $7$ .

$- 2 x < 2$

Step 3

Divide each term in $- 2 x < 2$ by $- 2$ and simplify.

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Step 3.1

Divide each term in $- 2 x < 2$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $x$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $2$ by $- 2$ .

$x > - 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > - 1$

Interval Notation:

$(- 1, \infty)$