Question

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

3x + 1 > 7 and 4x less than or equal to 24


A. a number line with an open circle on 2, a closed circle on 6, and shading in between.

B. a number line with an open circle on 2, shading to the left, and a closed circle on 6, and shading to the right.

C. a number line with a closed circle on 2, shading to the left, and open circle on 6, and shading to the right.

D. a number line with a closed circle on 2, an open circle on 6, and shading in between.

Answer 1

Option: A is the correct answer.

A. a number line with an open circle on 2, a closed circle on 6, and shading in between.

Explanation:

We are given a system of inequalities as:

3x + 1 > 7 and 4x less than or equal to 24

i.e. it could also be written as:

`3x+1>7\\\\3x>7-1\\\\3x>6\\\\x>2`

And the second inequality is:

`4x\leq 24\\\\x\leq 6`

Hence, the compound inequality could be represented as:

x>2 i.e. (2,∞)

and x≤6 i.e. (-∞,6]

Hence, the feasible region or the region that is common to both the inequalities is:

(2,6]

Hence, there will be a number line with open circle at 2 since 2 is not included in the domain and a closed circle at 6 and shading in between

Answer 2

we have

`3x+1 > 7`-------> inequality A

`4x\leq 24` -------> inequality B

Step 1

Solve inequality A

`3x+1 > 7\\ \\3x > 7-1 \\ \\x> 2`

the solution is the interval------> (2,∞)

Step 2

Solve inequality B

`4x\leq 24\\ \\x\leq 6`

the solution is the interval------> (-∞,6]

Step 3

Find the solution of the compound inequality

Solution A ∩ Solution B

(2,∞) ∩ (-∞,6]=(2,6]

therefore

the answer is the option A

a number line with an open circle on 2, a closed circle on 6, and shading in between