Solve the Inequality for z z/-4>=2

$\frac{z}{- 4} \geq 2$

Step 1

Multiply both sides by $- 4$ .

$\frac{z}{- 4} \cdot - 4 \leq 2 \cdot - 4$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{z}{- 4} \cdot - 4$ .

Cancel the common factor of $4$ .

Factor $4$ out of $- 4$ .

$\frac{z}{4 (- 1)} \cdot - 4 \leq 2 \cdot - 4$

Factor $4$ out of $- 4$ .

$\frac{z}{4 \cdot - 1} \cdot (4 \cdot - 1) \leq 2 \cdot - 4$

Cancel the common factor.

$\frac{z}{4 \cdot - 1} \cdot (4 \cdot - 1) \leq 2 \cdot - 4$

Rewrite the expression.

$\frac{z}{- 1} \cdot - 1 \leq 2 \cdot - 4$

Combine $\frac{z}{- 1}$ and $- 1$ .

$\frac{z \cdot - 1}{- 1} \leq 2 \cdot - 4$

Simplify the expression.

Move the negative one from the denominator of $\frac{z \cdot - 1}{- 1}$ .

$- 1 \cdot (z \cdot - 1) \leq 2 \cdot - 4$

Rewrite $- 1 \cdot (z \cdot - 1)$ as $- (z \cdot - 1)$ .

$- (z \cdot - 1) \leq 2 \cdot - 4$

Move $- 1$ to the left of $z$ .

$- (- 1 \cdot z) \leq 2 \cdot - 4$

Rewrite $- 1 z$ as $- z$ .

$- - z \leq 2 \cdot - 4$

Multiply $- - z$ .

Multiply $- 1$ by $- 1$ .

$1 z \leq 2 \cdot - 4$

Multiply $z$ by $1$ .

$z \leq 2 \cdot - 4$

Simplify the right side.

Multiply $2$ by $- 4$ .

$z \leq - 8$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$z \leq - 8$

Interval Notation:

$(- \infty, - 8]$