Solve the System of Inequalities x-6<6 and x+4>=-1

$x - 6 < 6$ and $x + 4 \geq - 1$

Step 1

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

Add $6$ to both sides of the inequality.

$x < 6 + 6$ and $x + 4 \geq - 1$

Add $6$ and $6$ .

$x < 12$ and $x + 4 \geq - 1$

Step 2

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

Subtract $4$ from both sides of the inequality.

$x < 12$ and $x \geq - 1 - 4$

Subtract $4$ from $- 1$ .

$x < 12$ and $x \geq - 5$

Step 3

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

$- 5 \leq x < 12$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 5 \leq x < 12$

Interval Notation:

$[- 5, 12)$

Step 5