Question

Choose the correct description of the graph of the compound inequality:

x − 3 < −9 or x + 5 greater than or equal to 12

A number line with a closed circle on −6, shading to the left, and an open circle on 7, shading to the right

A number line with an open circle on −6, a closed circle on 7, and shading in between

A number line with an open circle on −6, shading to the left, and a closed circle on 7, shading to the right

A number line with a closed circle on −6, an open circle on 7, and shading in between

Answer 1

x - 3 < -9 x + 5 > = 12
x < - 9 + 3 x > = 12 - 5
x < - 6 x > = 7

open circle on -6, shaded to the left.....closed circle on 7, shaded to the right

Answer 2

Answer with explanation:

The compound Inequality is:

1. x -3 < - 9

Adding 3 to both sides

x -3 + 3 < -9 + 3

x < -6

x ∈ (-∞,-6)

2. x + 5 ≥ 12

Subtracting ,5 from both sides

x +5 -5 ≥ 12 -5

x ≥ 7

x ∈ [7 , ∞)

Combining , solution of inequality 1 and inequality ,2

→→x ∈ (-∞,-6) ∪x ∈ [7 , ∞)

Depicting on the number line ,the solution set

Option C: A number line with an open circle on −6, shading to the left, and a closed circle on 7, shading to the right