Question

Which of the following options correctly represents the compound inequality 2(x + 4) < 6 or -X - 35 < -7?

A) 2x + 8 < 6 or -x - 35 < -7
B) 2x + 8 < 6 or -x - 35 > -7
C) 2x + 8 > 6 or -x - 35 < -7
D) 2x + 8 > 6 or -x - 35 > -7

Answer 1

Option A, 2x + 8 < 6 or -x - 35 < -7, is the correct representation of the compound inequality 2(x + 4) < 6 or -X - 35 < -7 after distributing and simplifying both parts of the inequality.

Step-by-step explanation:

The compound inequality given is 2(x + 4) < 6 or -X - 35 < -7. To find the correct representation, distribute and simplify both inequalities:

• For the first inequality, 2(x + 4) < 6, distribute 2 to both x and 4 to get 2x + 8 < 6.
• For the second inequality, -X - 35 < -7, you don't need to do any distribution.

Now, compare the options provided. The correct representation will match these simplified inequalities:

• Option A: 2x + 8 < 6 or -x - 35 < -7 is the exact match to our simplified expressions.

Therefore, Option A correctly represents the compound inequality 2(x + 4) < 6 or -X - 35 < -7.