Solve for x 0<3(x+9)<=26

$0 < 3 (x + 9) \leq 26$

Step 1

Apply the distributive property.

$0 < 3 x + 3 \cdot 9 \leq 26$

Step 2

Multiply $3$ by $9$ .

$0 < 3 x + 27 \leq 26$

Step 3

Move all terms not containing $x$ from the center section of the inequality.

Subtract $27$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$0 - 27 < 3 x \leq 26 - 27$

Subtract $27$ from $0$ .

$- 27 < 3 x \leq 26 - 27$

Subtract $27$ from $26$ .

$- 27 < 3 x \leq - 1$

Step 4

Divide each term in the inequality by $3$ .

$\frac{- 27}{3} < \frac{3 x}{3} \leq \frac{- 1}{3}$

Step 5

Divide $- 27$ by $3$ .

$- 9 < \frac{3 x}{3} \leq \frac{- 1}{3}$

Step 6

Cancel the common factor of $3$ .

Cancel the common factor.

$- 9 < \frac{3 x}{3} \leq \frac{- 1}{3}$

Divide $x$ by $1$ .

$- 9 < x \leq \frac{- 1}{3}$

Step 7

Move the negative in front of the fraction.

$- 9 < x \leq - \frac{1}{3}$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$- 9 < x \leq - \frac{1}{3}$

Interval Notation:

$(- 9, - \frac{1}{3}]$

Step 9