Question

Solve the inequality{1}/{x} + {1}/{3} < {1}/{5} forx:

a)x > 15
b)x > -15
c)x < -15
d)x < 15

Answer 1

The inequality 1/x + 1/3 < 1/5 is solved by finding a common denominator, rearranging terms, and isolating x, resulting in x < -7.5. Since x cannot be zero, the correct answer that fits the condition is x < 0.

Step-by-step explanation:

To solve the inequality 1/x + 1/3 < 1/5, let's first find a common denominator and combine the terms on the left side:

• 
  
• Multiply each term by 15x to avoid fractions:
  
  15 + 5x < 3x
• 
  
• Rearrange the inequality to isolate x:
  
  5x - 3x < -15
• 
  
• Simplify the inequality:
  
  2x < -15
• 
  
• Divide by 2 to find x:
  
  x < -7.5

However, we need to consider the original inequality to ensure we do not include any values that would make the denominator zero. Since x cannot be zero, the solution preserving the inequality while excluding zero is x < -7.5

Option (c) x < -15, is misleading because it includes values that are less than, but not close to, -7.5. Hence, the correct answer could be x < 0 as it fits the condition x cannot be zero and x must be less than -7.5.