Algebra Examples

$- 2 | 1 + 3 x | < 8$

Step 1

Divide each term in $- 2 | 1 + 3 x | < 8$ by $- 2$ and simplify.

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Step 1.1

Divide each term in $- 2 | 1 + 3 x | < 8$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 | 1 + 3 x |}{- 2} > \frac{8}{- 2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $- 2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{- 2 | 1 + 3 x |}{- 2} > \frac{8}{- 2}$

Step 1.2.1.2

Divide $| 1 + 3 x |$ by $1$ .

$| 1 + 3 x | > \frac{8}{- 2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $8$ by $- 2$ .

$| 1 + 3 x | > - 4$

Step 2

Since $| 1 + 3 x |$ is always positive and $- 4$ is negative, $| 1 + 3 x |$ is always greater than $- 4$ so the inequality is always true for any value of $x$ .

All real numbers

Step 3

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$