Question

Choose the correct description of the graph of the compound inequality 3x + 1 > 10 and 4x 20.

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

B. A number line with an open circle on 3, shading to the left and a closed circle on 5, shading to the right

C. A number line with an closed circle on 3, shading to the left, and a open circle on 5, and shading to the right

D. A number line with a closed circle on 3, an open circle on 5, with shading in between.

Answer 1

A number line with an open circle on 3, a closed circle on 5, and shading in between

Answer 2

we have in this problem

`3x+1 > 10` ------> inequality
`1`

`4x \leq 20` ------> inequality
`2`

Solve the inequality
`1`

`3x+1 > 10\\ 3x > 10-1\\ 3x > 9\\ x > 3`

the solution is the interval------> (3,∞)

Solve the inequality
`2`

`4x \leq 20\\\\ x \leq (20)/(4) \\\\ x \leq 5`

the solution is the interval------> (-∞,5]

Find the solution for the system

(3,∞) ∩ (-∞,5]--------> (3,5]

therefore

the answer is the option

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