Solve the System of Inequalities x-4>=4 and 6>=x-4

$x - 4 \geq 4$ and $6 \geq x - 4$

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

Add $4$ to both sides of the inequality.

$x \geq 4 + 4$

Add $4$ and $4$ .

$x \geq 8$

Simplify the second inequality.

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

$x - 4 \leq 6$

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

Add $4$ to both sides of the inequality.

$x \leq 6 + 4$

Add $6$ and $4$ .

$x \leq 10$

The intersection consists of the elements that are contained in both intervals.

$8 \leq x \leq 10$

The result can be shown in multiple forms.

Inequality Form:

$8 \leq x \leq 10$

Interval Notation:

$[8, 10]$