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emmasim [6.3K]
2 years ago
5

State all integer values of x in the interval (-2,5) that satisfy the following

Mathematics
1 answer:
dimaraw [331]2 years ago
5 0

Answer:

The only value in the interval (-2, 5) which satisfies the inequality is:

  • x = -1

Step-by-step explanation:

Given the inequality

  • -4x – 1 > 1
  • interval = (-2,5)

The integer values lie in the interval (-2, 5) = -1, 0, 1, 2, 3, 4

Let us substitute all the integer values lie in the interval

substitute x = -1

-4x – 1 > 1

-4(-1) - 1 > 1

4 - 1 > 1

3 > 1

TRUE

substitute x = 0

-4x – 1 > 1

-4(0) - 1 > 1

0 - 1 > 1

-1 > 1

FALSE

substitute x = 1

-4x – 1 > 1

-4(1) - 1 > 1

-4 - 1 > 1

-5 > 1

FALSE

substitute x = 2

-4x – 1 > 1

-4(2) - 1 > 1

-8 - 1 > 1

-7 > 1

FALSE

substitute x = 3

-4x – 1 > 1

-4(3) - 1 > 1

-12 - 1 > 1

-13 > 1

FALSE

substitute x = 4

-4x – 1 > 1

-4(4) - 1 > 1

-16 - 1 > 1

-17 > 1

FALSE

Therefore, the only value in the interval (-2, 5) which satisfies the inequality is:

  • x = -1
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