Question

Choose the correct description of the graph of the compound inequality x − 3 < −9 or x + 5 greater than or equal to 10.

Answer 1

x - 3 < 9    or    x + 5 ≥ 10
  + 3 + 3               - 5   - 5
     x < 12      or      x ≥ 5

Solution Set: {x|x < 12 or x ≥ 5}, (-∞, 12) or (5, ∞)

Answer 2

Answer:

A number line with an open circle on -6, shading to the left, and a closed circle on 5, shading to the right.

Step-by-step explanation:

The given compound inequality is

$x-3<-9$ or $x+5\geq 10$

We need to find the description of the graph of the compound inequality.

Solve each inequality.

$x-3<-9$

Add 3 on both sides.

$x-3+3<-9+3$

$x<-6$

The value of x is less that -6. Since -6 is not included in the solution set, therefore there is an open bracket at -6.

$x+5\geq 10$

Subtract 5 from both sides.

$x+5-5\geq 10-5$

$x\geq 5$

The value of x is greater than of equal to 5. Since 5 is included in the solution set, therefore there is a closed bracket at 5.

The solution of given compound inequality.

$(-\infty,-6)\cup [5,\infty)$

A number line with an open circle on -6, shading to the left, and a closed circle on 5, shading to the right.