Solve the Inequality for x -2/3x>=8

$- \frac{2}{3} x \geq 8$

Multiply each term in $- \frac{2}{3} x \geq 8$ by $- \frac{3}{2}$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{2}{3} x (- \frac{3}{2}) \leq 8 (- \frac{3}{2})$

Simplify the left side.

Combine $x$ and $\frac{2}{3}$ .

$- \frac{x \cdot 2}{3} (- \frac{3}{2}) \leq 8 (- \frac{3}{2})$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x \cdot 2}{3}$ into the numerator.

$\frac{- x \cdot 2}{3} (- \frac{3}{2}) \leq 8 (- \frac{3}{2})$

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{- x \cdot 2}{3} \cdot \frac{- 3}{2} \leq 8 (- \frac{3}{2})$

Factor $2$ out of $- x \cdot 2$ .

$\frac{2 \cdot (- x)}{3} \cdot \frac{- 3}{2} \leq 8 (- \frac{3}{2})$

Cancel the common factor.

$\frac{2 \cdot (- x)}{3} \cdot \frac{- 3}{2} \leq 8 (- \frac{3}{2})$

Rewrite the expression.

$\frac{- x}{3} \cdot - 3 \leq 8 (- \frac{3}{2})$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$\frac{- x}{3} \cdot (3 (- 1)) \leq 8 (- \frac{3}{2})$

Cancel the common factor.

$\frac{- x}{3} \cdot (3 \cdot - 1) \leq 8 (- \frac{3}{2})$

Rewrite the expression.

$- x \cdot - 1 \leq 8 (- \frac{3}{2})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x \leq 8 (- \frac{3}{2})$

Multiply $x$ by $1$ .

$x \leq 8 (- \frac{3}{2})$

Simplify the right side.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$x \leq 8 (\frac{- 3}{2})$

Factor $2$ out of $8$ .

$x \leq 2 (4) \frac{- 3}{2}$

Cancel the common factor.

$x \leq 2 \cdot 4 \frac{- 3}{2}$

Rewrite the expression.

$x \leq 4 \cdot - 3$

Multiply $4$ by $- 3$ .

$x \leq - 12$

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 12$

Interval Notation:

$(- \infty, - 12]$

Solve the Inequality for x -2/3x>=8

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