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

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

Step 1

Simplify $2 (x - 3)$ .

Start simplifying.

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

Simplify by adding zeros.

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

Apply the distributive property.

$2 x + 2 \cdot - 3 \geq - 3 (- 3 + x)$

Multiply $2$ by $- 3$ .

$2 x - 6 \geq - 3 (- 3 + x)$

Step 2

Simplify $- 3 (- 3 + x)$ .

Apply the distributive property.

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

Multiply $- 3$ by $- 3$ .

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

Step 3

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

Add $3 x$ to both sides of the inequality.

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

Add $2 x$ and $3 x$ .

$5 x - 6 \geq 9$

Step 4

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

Add $6$ to both sides of the inequality.

$5 x \geq 9 + 6$

Add $9$ and $6$ .

$5 x \geq 15$

Step 5

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

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

$\frac{5 x}{5} \geq \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{15}{5}$

Divide $x$ by $1$ .

$x \geq \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$x \geq 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x \geq 3$

Interval Notation:

$[3, \infty)$

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

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