Question

What is the solution set for this inequality? -7x + 21 > -42

A) x < 3
B) x > 3
C) x ≤ 3
D) x ≥ 3

Answer 1

The solution set for the inequality -7x + 21 > -42, after using algebraic manipulation, is x < 9, which is not listed in the provided options. There may have been an error in the question or the options.

Step-by-step explanation:

The solution set for the inequality -7x + 21 > -42 can be found by solving for x using algebraic manipulation. Here are the steps:

1. Add 42 to both sides of the inequality: -7x + 21 + 42 > -42 + 42
2. Simplify both sides: -7x + 63 > 0
3. Subtract 63 from both sides: -7x > -63
4. Divide both sides by -7, remembering to flip the inequality sign because we are dividing by a negative number: x < 9.

Therefore, the solution set for the given inequality is x < 9.

However, the provided options do not include x < 9. There seems to be a mistake either within the options or in the understanding of the original inequality. Assuming the inequality was stated correctly, none of the options provided (A, B, C, D) is correct. A review of the original problem or options given may be necessary.