Solve the System of @WORD 8<=2x<x+7

$8 \leq 2 x < x + 7$

Step 1

Solve $8 \leq 2 x$ for $x$ .

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

$2 x \geq 8$

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

Move all terms containing $x$ to the left side of the inequality.

Subtract $x$ from both sides of the inequality.

$2 x - x < 7$

Subtract $x$ from $2 x$ .

$x < 7$

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