Question

Twice the sum of a number and 7 is more than 6 or at most -3. Which compound inequality can represent this relationship

A. 2(x + 7) > 6 and 2(x + 7) <= - 3
B. 2(x + 7) < 6 or 2(x + 7) >= - 3
C. 2(x + 7) > 6 or 2(x + 7) <= - 3
D. 2(x + 7) < 6 and 2(x + 7) >= - 3

Answer 1

The compound inequality that corresponds to the statement is '2(x + 7) > 6 or 2(x + 7) ≤ -3', showcasing the two scenarios depicted in the condition separately and then combining them with an 'or'.

Step-by-step explanation:

The correct compound inequality that represents the relationship 'Twice the sum of a number and 7 is more than 6 or at most -3' is C. 2(x + 7) > 6 or 2(x + 7) ≤ -3. To solve the inequality, we can break it down into two separate parts and then combine them as a compound inequality:

1. For the 'more than 6' part, we set up the inequality 2(x + 7) > 6.
2. For the 'at most -3' part, we set up the inequality 2(x + 7) ≤ -3.

The word 'or' in the statement indicates that we should combine these inequalities with the 'or' conjunction, resulting in the correct answer as above.