Question

-(x - 5) - 9 < 3x + 42.

A) x > -10
B) x < -10
C) x < 10
D) x > 10

Answer 1

By distributing the negative sign and combining like terms, we simplify the given inequality to x > -11.5. Therefore, the correct answer is A) x > -10 which is less precise than -11.5 but is the closest option provided.

Step-by-step explanation:

We have been given the inequality -(x - 5) - 9 < 3x + 42. Our first step is to simplify the inequality by distributing the negative sign and combining like terms. Here is the step-by-step simplification:

• Distribute the negative sign: -x + 5 - 9 < 3x + 42
• Combine like terms: -x - 4 < 3x + 42
• Add x to both sides: -4 < 4x + 42
• Subtract 42 from both sides: -46 < 4x
• Divide both sides by 4: -11.5 < x, which means x > -11.5

Since x > -11.5, the correct answer is A) x > -10, as the options given are less precise than what we found.