Solve the System of @WORD -4<=2x-6<=12

$- 4 \leq 2 x - 6 \leq 12$

Step 1

Solve $- 4 \leq 2 x - 6$ for $x$ .

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

$2 x - 6 \geq - 4$

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

Add $6$ to both sides of the inequality.

$2 x \geq - 4 + 6$

Add $- 4$ and $6$ .

$2 x \geq 2$

Divide each term in $2 x \geq 2$ by $2$ and simplify.

Divide each term in $2 x \geq 2$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $2$ by $2$ .

$x \geq 1$

Step 2

Solve $2 x - 6 \leq 12$ for $x$ .

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

Add $6$ to both sides of the inequality.

$2 x \leq 12 + 6$

Add $12$ and $6$ .

$2 x \leq 18$

Divide each term in $2 x \leq 18$ by $2$ and simplify.

Divide each term in $2 x \leq 18$ by $2$ .

$\frac{2 x}{2} \leq \frac{18}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{18}{2}$

Divide $x$ by $1$ .

$x \leq \frac{18}{2}$

Simplify the right side.

Divide $18$ by $2$ .

$x \leq 9$

Step 3

Find the intersection of $x \geq 1$ and $x \leq 9$ .

$1 \leq x \leq 9$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x \leq 9$

Interval Notation:

$[1, 9]$

Step 5

Solve the System of @WORD -4<=2x-6<=12

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