Solve the System of Inequalities -2<=2x-4<4

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

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

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

$2 x - 4 \geq - 2$

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

Add $4$ to both sides of the inequality.

$2 x \geq - 2 + 4$

Add $- 2$ and $4$ .

$2 x \geq 2$

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 $2$ .

$x \geq 1$

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

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

Add $4$ to both sides of the inequality.

$2 x < 4 + 4$

Add $4$ and $4$ .

$2 x < 8$

Divide each term in $2 x < 8$ by $2$ and simplify.

Divide each term in $2 x < 8$ by $2$ .

$\frac{2 x}{2} < \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{8}{2}$

Divide $x$ by $1$ .

$x < \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

$x < 4$

Find the intersection of $x \geq 1$ and $x < 4$ .

$1 \leq x < 4$

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x < 4$

Interval Notation:

$[1, 4)$

Solve the System of Inequalities -2<=2x-4<4

Related Questions

Support LCMGCF.com by disabling your adblocker.