Question

Solve the inequality -3 < -4(x-14) < -13 in interval notation:

a) (10, 11)
b) (11, 12)
c) (12, 13)
d) (13, 14)

Answer 1

Solving the inequality leads to a contradiction, indicating that there is no solution. Therefore, none of the provided interval notations are correct.

Step-by-step explanation:

To solve the inequality -3 < -4(x-14) < -13, we need to isolate x in the middle. Let's solve the inequality in two parts, first the left side:

• 
  
• -3 < -4(x - 14)
• 
  
• Divide both sides by -4, remembering to reverse the inequality sign:
• 
  
• 3/4 > x - 14
• 
  
• Add 14 to both sides:
• 
  
• x < 14 + 3/4
• 
  
• x < 14.75

Now let's solve the right side:

• 
  
• -4(x - 14) < -13
• 
  
• Divide both sides by -4:
• 
  
• x - 14 > 13/4
• 
  
• Add 14 to both sides:
• 
  
• x > 14 + 13/4
• 
  
• x > 14 + 3.25
• 
  
• x > 17.25

As we can see, our process led to a contradiction, which means that the initial inequality has no solution. Therefore, none of the given interval options is the correct answer.