Solve the System of @WORD 9<=6x+6<18

$9 \leq 6 x + 6 < 18$

Step 1

Solve $9 \leq 6 x + 6$ for $x$ .

Rewrite so $x$ is on the left side of the inequality.

$6 x + 6 \geq 9$

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

Subtract $6$ from both sides of the inequality.

$6 x \geq 9 - 6$

Subtract $6$ from $9$ .

$6 x \geq 3$

Divide each term in $6 x \geq 3$ by $6$ and simplify.

Divide each term in $6 x \geq 3$ by $6$ .

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

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

Cancel the common factors.

Factor $3$ out of $6$ .

$x \geq \frac{3 \cdot 1}{3 \cdot 2}$

Cancel the common factor.

$x \geq \frac{3 \cdot 1}{3 \cdot 2}$

Rewrite the expression.

$x \geq \frac{1}{2}$

Step 2

Solve $6 x + 6 < 18$ for $x$ .

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

Subtract $6$ from both sides of the inequality.

$6 x < 18 - 6$

Subtract $6$ from $18$ .

$6 x < 12$

Divide each term in $6 x < 12$ by $6$ and simplify.

Divide each term in $6 x < 12$ by $6$ .

$\frac{6 x}{6} < \frac{12}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} < \frac{12}{6}$

Divide $x$ by $1$ .

$x < \frac{12}{6}$

Simplify the right side.

Divide $12$ by $6$ .

$x < 2$

Step 3

Find the intersection of $x \geq \frac{1}{2}$ and $x < 2$ .

$\frac{1}{2} \leq x < 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$\frac{1}{2} \leq x < 2$

Interval Notation:

$[\frac{1}{2}, 2)$

Step 5

Solve the System of @WORD 9<=6x+6<18

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