Solve the Inequality for x -1/2x>=4

$- \frac{1}{2} x \geq 4$

Multiply each term in $- \frac{1}{2} x \geq 4$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Combine $x$ and $\frac{1}{2}$ .

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- x \cdot - 1 \leq 4 \cdot - 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x \leq 4 \cdot - 2$

Multiply $x$ by $1$ .

$x \leq 4 \cdot - 2$

Simplify the right side.

Multiply $4$ by $- 2$ .

$x \leq - 8$

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 8$

Interval Notation:

$(- \infty, - 8]$

Solve the Inequality for x -1/2x>=4

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