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 < 12 or x ≥ 5, (-∞, 12) or (5, ∞)

Answer 2

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

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.