Algebra Examples

$- 3 < \frac{5 x - 1}{4} < 0$

Step 1

Multiply each term in the inequality by $4$ .

$- 3 \cdot 4 < \frac{5 x - 1}{4} \cdot 4 < 0 \cdot 4$

Step 2

Multiply $- 3$ by $4$ .

$- 12 < \frac{5 x - 1}{4} \cdot 4 < 0 \cdot 4$

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Cancel the common factor.

$- 12 < \frac{5 x - 1}{4} \cdot 4 < 0 \cdot 4$

Step 3.2

Rewrite the expression.

$- 12 < 5 x - 1 < 0 \cdot 4$

Step 4

Multiply $0$ by $4$ .

$- 12 < 5 x - 1 < 0$

Step 5

Move all terms not containing $x$ from the center section of the inequality.

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Step 5.1

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 12 + 1 < 5 x < 0 + 1$

Step 5.2

Add $- 12$ and $1$ .

$- 11 < 5 x < 0 + 1$

Step 5.3

Add $0$ and $1$ .

$- 11 < 5 x < 1$

Step 6

Divide each term in the inequality by $5$ .

$\frac{- 11}{5} < \frac{5 x}{5} < \frac{1}{5}$

Step 7

Move the negative in front of the fraction.

$- \frac{11}{5} < \frac{5 x}{5} < \frac{1}{5}$

Step 8

Cancel the common factor of $5$ .

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Step 8.1

Cancel the common factor.

$- \frac{11}{5} < \frac{5 x}{5} < \frac{1}{5}$

Step 8.2

Divide $x$ by $1$ .

$- \frac{11}{5} < x < \frac{1}{5}$

Step 9

The result can be shown in multiple forms.

Inequality Form:

$- \frac{11}{5} < x < \frac{1}{5}$

Interval Notation:

$(- \frac{11}{5}, \frac{1}{5})$

Step 10