Solve the System of @WORD -4<(2x-1)/4<0

$- 4 < \frac{2 x - 1}{4} < 0$

Step 1

Solve $- 4 < \frac{2 x - 1}{4}$ for $x$ .

Multiply both sides by $4$ .

$- 4 \cdot 4 < \frac{2 x - 1}{4} \cdot 4$

Simplify.

Simplify the left side.

Multiply $- 4$ by $4$ .

$- 16 < \frac{2 x - 1}{4} \cdot 4$

Simplify the right side.

Cancel the common factor of $4$ .

Cancel the common factor.

$- 16 < \frac{2 x - 1}{4} \cdot 4$

Rewrite the expression.

$- 16 < 2 x - 1$

Solve for $x$ .

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

$2 x - 1 > - 16$

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

Add $1$ to both sides of the inequality.

$2 x > - 16 + 1$

Add $- 16$ and $1$ .

$2 x > - 15$

Divide each term in $2 x > - 15$ by $2$ and simplify.

Divide each term in $2 x > - 15$ by $2$ .

$\frac{2 x}{2} > \frac{- 15}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{- 15}{2}$

Divide $x$ by $1$ .

$x > \frac{- 15}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{15}{2}$

Step 2

Solve $\frac{2 x - 1}{4} < 0$ for $x$ .

Multiply both sides by $4$ .

$\frac{2 x - 1}{4} \cdot 4 < 0 \cdot 4$

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{2 x - 1}{4} \cdot 4 < 0 \cdot 4$

Rewrite the expression.

$2 x - 1 < 0 \cdot 4$

Simplify the right side.

Multiply $0$ by $4$ .

$2 x - 1 < 0$

Solve for $x$ .

Add $1$ to both sides of the inequality.

$2 x < 1$

Divide each term in $2 x < 1$ by $2$ and simplify.

Divide each term in $2 x < 1$ by $2$ .

$\frac{2 x}{2} < \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{1}{2}$

Divide $x$ by $1$ .

$x < \frac{1}{2}$

Step 3

Find the intersection of $x > - \frac{15}{2}$ and $x < \frac{1}{2}$ .

$- \frac{15}{2} < x < \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- \frac{15}{2} < x < \frac{1}{2}$

Interval Notation:

$(- \frac{15}{2}, \frac{1}{2})$

Step 5

Solve the System of @WORD -4<(2x-1)/4<0

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