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Right now we are learning about absolute value inequalities. I have to solve and graph this inequality:

Pretend my paranpheses are absolute value signs

(x-4) + 5 is greater than or equal to 10.

I assume I would take 5 away from each side first. But what would be the correct way to display this on a line, and what would be its set builder notation and interval notation?

Thank you so much! :-)

  • Here's what I got... -

    I took away 5 from each side and added 4 to each side. That got me

    (x) is greater than or equal to 14.

    Would this make the set builder notation be:

    {x such as x is greater than or equal to 4}

    And the interval notation be:

    (negative infinity, 14] U [14, infinity)?

    Thanks! :-)

  • Algebra -

    You have to consider two cases. I will leave out the = sign for convenience.
    (1) If x - 4 > 0, then
    x - 4 + 5 > 10
    x > 9 (which satisfies the x>4 assumption)

    (2) If x - 4 < 0, then
    If 4 - x + 5 > 10, then
    -x > 1
    x < -1
    (which satisfies the x<4 assumption)

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