Solve the Inequality for x 3(x+3)<=5x-3

$3 (x + 3) \leq 5 x - 3$

Simplify $3 (x + 3)$ .

Rewrite.

$0 + 0 + 3 (x + 3) \leq 5 x - 3$

Simplify by adding zeros.

$3 (x + 3) \leq 5 x - 3$

Apply the distributive property.

$3 x + 3 \cdot 3 \leq 5 x - 3$

Multiply $3$ by $3$ .

$3 x + 9 \leq 5 x - 3$

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

Subtract $5 x$ from both sides of the inequality.

$3 x + 9 - 5 x \leq - 3$

Subtract $5 x$ from $3 x$ .

$- 2 x + 9 \leq - 3$

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

Subtract $9$ from both sides of the inequality.

$- 2 x \leq - 3 - 9$

Subtract $9$ from $- 3$ .

$- 2 x \leq - 12$

Divide each term in $- 2 x \leq - 12$ by $- 2$ and simplify.

Divide each term in $- 2 x \leq - 12$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \geq \frac{- 12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \geq \frac{- 12}{- 2}$

Divide $x$ by $1$ .

$x \geq \frac{- 12}{- 2}$

Simplify the right side.

Divide $- 12$ by $- 2$ .

$x \geq 6$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 6$

Interval Notation:

$[6, \infty)$

Solve the Inequality for x 3(x+3)<=5x-3

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