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

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

User Franchesco
by
8.8k points

1 Answer

2 votes

Final answer:

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.

User Anya Hope
by
8.4k points

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