Final answer:
To solve the compound inequality 5 < 3x < 20, we divide all parts by 3 to get 5/3 < x < 20/3. The correct number line will show a segment from just after 5/3 to just before 20/3, without including the endpoints.
Step-by-step explanation:
You are asking which number line represents the solution to the compound inequality 5 < 3x < 20. To solve this, first, you divide all parts of the inequality by 3, because the variable x is being multiplied by 3. This will isolate x and give us the inequality 5/3 < x < 20/3. Therefore, the solution set for x is all real numbers that are greater than 5/3 and less than 20/3.
On a number line, this will be indicated as a line or segment that starts just after 5/3 and ends just before 20/3, without including the endpoints since the inequality does not include the equality (i.e. x is not equal to 5/3 or 20/3).
Without the actual number lines labeled A, B, C, or D, I cannot point out which specific one is correct. However, I have laid out the process to determine this. Please look at your number lines and select the one that shows a segment starting slightly after 5/3 and ending slightly before 20/3.