Question

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

x − 3 < −7 or x + 5 greater than or equal to 8

A.A number line with an open circle on −4, shading to the left, and a closed circle on 3, shading to the right

B.A number line with a closed circle on −4, shading to the left, and an open circle on 3, shading to the right

C. A number line with an open circle on −4, a closed circle on 3, and shading in between

D.A number line with a closed circle on −4, an open circle on 3, and shading in between

Answer 1

A. A number line with an open circle on -4, shading to the left, and a closed circle on 3, shading to the right

Answer 2

we have the compound inequality

`x-3 < -7` --------> inequality A

`x < -7+3`

`x < -4`

The solution inequality A is the interval-------> (-∞,-4)

A number line with an open circle on
`-4`, shading to the left

`x+5 \geq 8` --------> inequality B

`x \geq 8-5`

`x \geq 3`

The solution inequality B is the interval--------> [3,∞)

A number line with a closed circle on
`3`, shading to the right

so

The solution inequality A or inequality B is equal to

Solution A +Solution B=(-∞,-4) + [3,∞)

therefore

the answer is the option A

A number line with an open circle on −4, shading to the left, and a closed circle on 3, shading to the right