Solve the System of @WORD -12<=2x-4<10

$- 12 \leq 2 x - 4 < 10$

Step 1

Solve $- 12 \leq 2 x - 4$ for $x$ .

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

$2 x - 4 \geq - 12$

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

Add $4$ to both sides of the inequality.

$2 x \geq - 12 + 4$

Add $- 12$ and $4$ .

$2 x \geq - 8$

Divide each term in $2 x \geq - 8$ by $2$ and simplify.

Divide each term in $2 x \geq - 8$ by $2$ .

$\frac{2 x}{2} \geq \frac{- 8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{- 8}{2}$

Divide $x$ by $1$ .

$x \geq \frac{- 8}{2}$

Simplify the right side.

Divide $- 8$ by $2$ .

$x \geq - 4$

Step 2

Solve $2 x - 4 < 10$ for $x$ .

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

Add $4$ to both sides of the inequality.

$2 x < 10 + 4$

Add $10$ and $4$ .

$2 x < 14$

Divide each term in $2 x < 14$ by $2$ and simplify.

Divide each term in $2 x < 14$ by $2$ .

$\frac{2 x}{2} < \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{14}{2}$

Divide $x$ by $1$ .

$x < \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$x < 7$

Step 3

Find the intersection of $x \geq - 4$ and $x < 7$ .

$- 4 \leq x < 7$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 4 \leq x < 7$

Interval Notation:

$[- 4, 7)$

Step 5

Solve the System of @WORD -12<=2x-4<10

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