Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Doing College Algebra and came across a Tricky Problem?

l(3x-2)divided by 5l is less then or equal to 1/2 

and i'm doing inequalities in one variable (intermediate algebra eight edition)the lines on both sides are absolute value symbols

Update:

Yes it is the second thing you said

Update 2:

Thank you

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  • 1 month ago
    Favourite answer

    is that 

    l(3x-2)/5l ≤ 1/2 

    but what is the question?

    solve for x?

    ((3x-2)/5)² ≤ 1/4

    (9x² – 12x + 4)/25 ≤ 1/4

    9x² – 12x + 4 ≤ 25/4

    36x² – 48x + 16 ≤ 25

    36x² – 48x – 9 ≤ 0

    12x² – 16x – 3 ≤ 0

    (2x – 3)(6x + 1) ≤ 0

    find critical points, which are x = +3/2 and –1/6

    Check intervals in between critical points. 

    (Test values in the intervals to see if they work.)

    x ≤ –1/6

    l(3x-2)/5l ≤ 1/2 

    l(3(–1)-2)/5l ≤ 1/2 

    l(–5)/5l ≤ 1/2 

    1 ≤ 1/2 NO

    (Doesn't work in original inequality)

    –1/6 ≤ x ≤ 3/2

    l(3x-2)/5l ≤ 1/2 

    l(3(1)-2)/5l ≤ 1/2 

    l(1)/5l ≤ 1/2 

    1/5 ≤ 1/2 ok

    (Works in original inequality)

    x ≥ 3/2

    l(3•2-2)/5l ≤ 1/2 

    l(4)/5l ≤ 1/2 

    4/5 ≤ 1/2 NO

    (Doesn't work in original inequality)

    answer

    –1/6 ≤ x ≤ 3/2

  • 1 month ago

    Here's how I interpreted your inequality:

    |(3x - 2)/5| ≤ 1/2

    If you take off the absolute value symbols, the value must be between -1/2 and 1/2:

    -1/2 ≤ (3x - 2)/5 ≤ 1/2

    We're trying to isolate x in the middle, so start by multiplying everything by 5:

    -5/2 ≤ 3x - 2 ≤ 5/2

    Add 2 everywhere:

    2 - 5/2 ≤ 3x ≤ 2 + 5/2

    Simplify the outside values:

    4/2 - 5/2 ≤ 3x ≤ 4/2 + 5/2

    -1/2 ≤ 3x ≤ 9/2

    Divide everything by 3 to finally get x alone:

    -1/6 ≤ x ≤ 9/6

    Reduce the fraction:

    -1/6 ≤ x ≤ 3/2

    Or:

    -1/6 ≤ x ≤ 1½

  • Anonymous
    1 month ago

    Oh I did that a few years ago but don't remember anything sorry :(

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