Question

20%2B%2014find%20%5C%3A%20all%20%5C%3A%20the%20%5C%3A%20prime%20%5C%3A%20numbers%20%5C%3A%20that%20%5C%3A%20signify%20%5C%3A%20the%20%5C%3A%20inequality" id="TexFormula1" title="given \: that2 \leqslant 5 \times - 8 \leqslant \times + 14find \: all \: the \: prime \: numbers \: that \: signify \: the \: inequality" alt="given \: that2 \leqslant 5 \times - 8 \leqslant \times + 14find \: all \: the \: prime \: numbers \: that \: signify \: the \: inequality" align="absmiddle" class="latex-formula">
find all the prime numbers that Satisfy the inequality.​

Answer 1

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

__

right part

  5x -8 ≤ x +14

  4x ≤ 22 . . . . . add 8-x

  x ≤ 5.5 . . . . . divide by 4

__

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

  x = {2, 3, 5}