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-14is less then and equal to 3x -7less than and equal to -2

  • math - ,

    Write
    -14 <= 3x-7 <= -2
    or
    -14 ≤ 3x-7 ≤ -2

    (≤ is written as "& l e ;" without the double quotes and without spaces).

    There are two inequalities. We need to solve each one separately and find the solution interval that satisfies both inequalities.

    -14 ≤ 3x-7
    => 3x-7 ≥ -14
    => 3x ≥ -14 + 7 = -7
    => x ≥ -7/3

    3x-7 ≤ -2
    => 3x ≤ -2+7 = 5
    => x ≤ 5/3

    Take the most restrictive interval to give
    -7/3 ≤ x ≤ 5/3

    Check the solution by substituting it back to the original inequalities.

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