Question

Solve. 2x + 7 ≥ 27 or 3 + 3x ≤ 30

A) 10 ≤ x ≤ 9
B) x ≥ 10 or x ≤ 9
C) x ≥ 17 or x ≤ 11
D) x ≤ −10 or x ≤ 9

Answer 1

Solving the compound inequality results in the solution x ≥ 10 or x ≤ 9, which means that any x that is greater than or equal to 10 or less than or equal to 9 is part of the solution set.

Step-by-step explanation:

To solve the compound inequality 2x + 7 ≥ 27 or 3 + 3x ≤ 30, we begin by isolating x in each inequality. For the first inequality, subtract 7 from both sides to get 2x ≥ 20, then divide by 2 to get x ≥ 10.

For the second inequality, we subtract 3 from both sides to get 3x ≤ 27, then divide by 3 to get x ≤ 9.

Since the inequalities are connected by 'or', we combine the solutions to get the final answer x ≥ 10 or x ≤ 9, which corresponds to option B).

You should always eliminate terms wherever possible to simplify the algebra and check your answer to ensure it is reasonable.