Question

Solve the inequality: -6(x + 4) > 18 or 4x + 5 > 33.

a) x > -7
b) x < -7
c) x > 7
d) x < 7

Answer 1

The solution to the inequalities -6(x + 4) > 18 and 4x + 5 > 33 is x < -7 or x > 7, which suggests there might be an error since neither option b or c alone is the complete solution; the correct answer would be a combination of x < -7 and x > 7.

Step-by-step explanation:

To solve the inequality -6(x + 4) > 18 or 4x + 5 > 33, we must treat each part of the 'or' statement separately and then find the union of the solutions. Let's start with the first inequality.

1. Divide both sides of the inequality -6(x + 4) > 18 by -6, remembering to reverse the inequality sign when dividing by a negative number, giving us x + 4 < -3.
2. Subtract 4 from both sides to isolate x, yielding x < -7.

Now, let's solve the second inequality.

1. Subtract 5 from both sides of the inequality 4x + 5 > 33, resulting in 4x > 28.
2. Divide both sides by 4 to solve for x, giving x > 7.

Combining the solutions, since the statement is an 'or' statement, x can be less than -7 or greater than 7. Therefore, the correct answer is x < -7 or x > 7, which is not one of the answer choices provided, suggesting there may be an error in the question. However, the closest option to the correct solution is x < -7 (option b) and x > 7 (option c) combined.