Solve for x 9-3x>=2(x-3)

$9 - 3 x \geq 2 (x - 3)$

Step 1

Simplify $2 (x - 3)$ .

Rewrite.

$9 - 3 x \geq 0 + 0 + 2 (x - 3)$

Simplify by adding zeros.

$9 - 3 x \geq 2 (x - 3)$

Apply the distributive property.

$9 - 3 x \geq 2 x + 2 \cdot - 3$

Multiply $2$ by $- 3$ .

$9 - 3 x \geq 2 x - 6$

Step 2

Move all terms containing $x$ to the left side of the inequality.

Subtract $2 x$ from both sides of the inequality.

$9 - 3 x - 2 x \geq - 6$

Subtract $2 x$ from $- 3 x$ .

$9 - 5 x \geq - 6$

Step 3

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

Subtract $9$ from both sides of the inequality.

$- 5 x \geq - 6 - 9$

Subtract $9$ from $- 6$ .

$- 5 x \geq - 15$

Step 4

Divide each term in $- 5 x \geq - 15$ by $- 5$ and simplify.

Divide each term in $- 5 x \geq - 15$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \leq \frac{- 15}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} \leq \frac{- 15}{- 5}$

Divide $x$ by $1$ .

$x \leq \frac{- 15}{- 5}$

Simplify the right side.

Divide $- 15$ by $- 5$ .

$x \leq 3$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq 3$

Interval Notation:

$(- \infty, 3]$

Solve for x 9-3x>=2(x-3)

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