Solve for x 9(x/3+1)>=6

$9 (\frac{x}{3} + 1) \geq 6$

Simplify.

Apply the distributive property.

$9 \frac{x}{3} + 9 \cdot 1 \geq 6$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$3 (3) \frac{x}{3} + 9 \cdot 1 \geq 6$

Cancel the common factor.

$3 \cdot 3 \frac{x}{3} + 9 \cdot 1 \geq 6$

Rewrite the expression.

$3 x + 9 \cdot 1 \geq 6$

Multiply $9$ by $1$ .

$3 x + 9 \geq 6$

Divide each term in $(3 x + 9) \geq 6$ by $9$ and simplify.

Divide each term in $(3 x + 9) \geq 6$ by $9$ .

$\frac{(3 x + 9)}{9} \geq \frac{6}{9}$

Simplify the left side.

Cancel the common factor of $3 x + 9$ and $9$ .

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 9}{9} \geq \frac{6}{9}$

Factor $3$ out of $9$ .

$\frac{3 x + 3 \cdot 3}{9} \geq \frac{6}{9}$

Factor $3$ out of $3 x + 3 \cdot 3$ .

$\frac{3 (x + 3)}{9} \geq \frac{6}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

$\frac{3 (x + 3)}{3 (3)} \geq \frac{6}{9}$

Cancel the common factor.

$\frac{3 (x + 3)}{3 \cdot 3} \geq \frac{6}{9}$

Rewrite the expression.

$\frac{x + 3}{3} \geq \frac{6}{9}$

Simplify the right side.

Cancel the common factor of $6$ and $9$ .

Factor $3$ out of $6$ .

$\frac{x + 3}{3} \geq \frac{3 (2)}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

$\frac{x + 3}{3} \geq \frac{3 \cdot 2}{3 \cdot 3}$

Cancel the common factor.

$\frac{x + 3}{3} \geq \frac{3 \cdot 2}{3 \cdot 3}$

Rewrite the expression.

$\frac{x + 3}{3} \geq \frac{2}{3}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x + 3 \geq 2$

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

Subtract $3$ from both sides of the inequality.

$x \geq 2 - 3$

Subtract $3$ from $2$ .

$x \geq - 1$

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 1$

Interval Notation:

$[- 1, \infty)$

Solve for x 9(x/3+1)>=6

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