Solve the System of Inequalities x+5<=1 or x-7>=-3

$x + 5 \leq 1$ or $x - 7 \geq - 3$

Step 1

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

Subtract $5$ from both sides of the inequality.

$x \leq 1 - 5$

Subtract $5$ from $1$ .

$x \leq - 4$

Step 2

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

Add $7$ to both sides of the inequality.

$x \geq - 3 + 7$

Add $- 3$ and $7$ .

$x \geq 4$

Step 3

The union consists of all of the elements that are contained in each interval.

$x \leq - 4$ or $x \geq 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 4 or x \geq 4$

Interval Notation:

$(- \infty, - 4] \cup [4, \infty)$

Step 5