Solve the System of Inequalities 3<=6x-3<=9

$3 \leq 6 x - 3 \leq 9$

Solve $3 \leq 6 x - 3$ for $x$ .

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

$6 x - 3 \geq 3$

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

Add $3$ to both sides of the inequality.

$6 x \geq 3 + 3$

Add $3$ and $3$ .

$6 x \geq 6$

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

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

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $6$ by $6$ .

$x \geq 1$

Solve $6 x - 3 \leq 9$ for $x$ .

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

Add $3$ to both sides of the inequality.

$6 x \leq 9 + 3$

Add $9$ and $3$ .

$6 x \leq 12$

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

Divide each term in $6 x \leq 12$ by $6$ .

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $12$ by $6$ .

$x \leq 2$

Find the intersection of $x \geq 1$ and $x \leq 2$ .

$1 \leq x \leq 2$

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x \leq 2$

Interval Notation:

$[1, 2]$

Solve the System of Inequalities 3<=6x-3<=9

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