Solve the Inequality for x x/-6-8<=-12

$\frac{x}{- 6} - 8 \leq - 12$

Step 1

Move the negative in front of the fraction.

$- \frac{x}{6} - 8 \leq - 12$

Step 2

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

Add $8$ to both sides of the inequality.

$- \frac{x}{6} \leq - 12 + 8$

Add $- 12$ and $8$ .

$- \frac{x}{6} \leq - 4$

Step 3

Divide each term in $- \frac{x}{6} \leq - 4$ by $- 1$ and simplify.

Divide each term in $- \frac{x}{6} \leq - 4$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{x}{6}}{- 1} \geq \frac{- 4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{x}{6}}{1} \geq \frac{- 4}{- 1}$

Divide $\frac{x}{6}$ by $1$ .

$\frac{x}{6} \geq \frac{- 4}{- 1}$

Simplify the right side.

Divide $- 4$ by $- 1$ .

$\frac{x}{6} \geq 4$

Step 4

Multiply both sides by $6$ .

$\frac{x}{6} \cdot 6 \geq 4 \cdot 6$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{x}{6} \cdot 6 \geq 4 \cdot 6$

Rewrite the expression.

$x \geq 4 \cdot 6$

Simplify the right side.

Multiply $4$ by $6$ .

$x \geq 24$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x \geq 24$

Interval Notation:

$[24, \infty)$

Solve the Inequality for x x/-6-8<=-12

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