Question

Choose the correct description of the graph of the compound inequality 3x + 1 > 10 and 4x less than or equal to 20 A number line with an open circle on 3, a closed circle on 5, and shading in between A number line with an open circle on 3, shading to the left, and a closed circle on 5, shading to the right A number line with a closed circle on 3, shading to the left, and an open circle on 5, and shading to the right A number line with a closed circle on 3, an open circle on 5, and shading in between

Answer 1

The graph is a number line with an open circle on 3, a closed circle on 5, and shading in between. Option 1

Explanation:

Answer 2

The graph is a number line with an open circle on 3, a closed circle on 5, and shading in between.

Explanation:

We need to check the graph of the compound inequality:

• 3 x+1>10

so on solving the first inequality

3x>10-1 (on subtracting both side by 1)

3x>9

x>3 ( on dividing both side by 3)

Hence, we get a region on a number line from (3,∞).

• 4 x≤20

this inequality could also be written as:

x≤5 ( dividing both side of the inequality with 5)

Hence, we get a region on a number line from (-∞,5].

Hence, the intersection region from both the inequality is obtained as:

(3,∞)∩(-∞,5]=(3,5]

Hence, The graph of this compound inequality is a number line with an open circle on 3, a closed circle on 5, and shading in between.

The graphs are also attached to the answer.