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solve the given inequality and graph its solution on the number line

2-x/3less than or eqaul to (</) 3-2x/5

lxl less than or equal to 5

2 is less than or eqaul to lx-6l less than or equal to 5

  • math -

    1.

    2 - x/3 < 3 - 2x/5
    multiply by 15, the LCD
    30 - 5x ≤ 45 - 6x
    6x - 5x ≤ 45-30
    x ≤ 15

    2.

    |x| ≤ 5
    x ≤ 5 AND -x≤5
    x≤5 AND x≥-5
    in short notation: -5 ≤ x ≤ 5

    3.

    2 ≤ |x-6| ≤ 5

    case1: 2 ≤ x-6≤ 5
    8 ≤ x ≤ 11

    case2:
    2 ≤ -x+6≤ 5
    -4 ≤ -x ≤ -1
    4 ≥ x ≥ 1 or
    1 ≤ x ≤ 4

    so 8 ≤ x ≤ 11 OR 1 ≤ x ≤ 4

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