Solve the Inequality for x 3(x-2)-9x+18<=0

$3 (x - 2) - 9 x + 18 \leq 0$

Step 1

Simplify $3 (x - 2) - 9 x + 18$ .

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot - 2 - 9 x + 18 \leq 0$

Multiply $3$ by $- 2$ .

$3 x - 6 - 9 x + 18 \leq 0$

Simplify by adding terms.

Subtract $9 x$ from $3 x$ .

$- 6 x - 6 + 18 \leq 0$

Add $- 6$ and $18$ .

$- 6 x + 12 \leq 0$

Step 2

Subtract $12$ from both sides of the inequality.

$- 6 x \leq - 12$

Step 3

Divide each term in $- 6 x \leq - 12$ by $- 6$ and simplify.

Divide each term in $- 6 x \leq - 12$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 x}{- 6} \geq \frac{- 12}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} \geq \frac{- 12}{- 6}$

Divide $x$ by $1$ .

$x \geq \frac{- 12}{- 6}$

Simplify the right side.

Divide $- 12$ by $- 6$ .

$x \geq 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 2$

Interval Notation:

$[2, \infty)$

Solve the Inequality for x 3(x-2)-9x+18<=0

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