[tex]given \: that2 \leqslant 5 \times - 8 \leqslant \times + 14find \: all \: the \: prime \: numbers \: that \: signify \: the \: inequality[/tex]
find all the prime numbers that Satisfy the inequality.​

Respuesta :

9514 1404 393

Answer:

  x = {2, 3, 5}

Step-by-step explanation:

Break the inequality into two parts:

left part

  2 ≤ 5x -8

  10 ≤ 5x . . . . . add 8

  2 ≤ x . . . . . . . divide by 5

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right part

  5x -8 ≤ x +14

  4x ≤ 22 . . . . . add 8-x

  x ≤ 5.5 . . . . . divide by 4

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The solution space is 2 ≤ x ≤ 5.5. The prime numbers in this range are ...

  x = {2, 3, 5}