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I have two different questions.

what is the set built notation of -11x-24<27-10x


write the slope intercept equation for the line with slope -5/6 and y intercept (0,4)

  • Math -

    -11x + 10x < 27 + 24
    -x < 51
    x > -51

    I will let you put into the notation you are familiar with

    second one:
    since you are given the slope and the y-intercept, the equation can be simply stated as

    y = (-5/6)x + 4

  • Math -

    -11x-24 < 27-10x
    combine similar terms:
    -11x + 10x < 27 + 24
    *when transposing terms to other side of equation, the sign must become the opposite*
    -x < 51
    multiply by -1 to get positive x:
    x > -51
    *note that when all terms are multiplied or divided by a NEGATIVE number, the inequality sign becomes the opposite*
    thus x is all real number greater than -51 or (-51, +infinity)

    for the second question,
    slope-intercept form is:
    y = mx + b
    where b is the y-intercept (y-coordinate of the y-intercept) and m is the slope,, thus:
    y = (-5/6)x + 4

    hope this helps. :)

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