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Math Help - Multi-Step Linear Inequalities

  1. #1
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    Multi-Step Linear Inequalities

    i got every problem right on these things, except for ones involving Fractions. i thought i had it, but...
    here's the ones i missed. (note: 1/2=one half, idk how to do fractions.) i tried to divide by the fraction, which went badly, and ended up with huge decimals...so i guess that wasnt right.
    Also, i don't know how to do a Greater than or equal to, or a less than or equal to, sign, so i'm just going to use <(=) or >(=)

    2/3x + 3 >(=) 11

    6 >(=) 7/3x - 1

    -1/2x + 3 < 7

    thanks in advance
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  2. #2
    Super Member Aryth's Avatar
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    Let's look at the first one:

    \frac{2}{3}x + 3 \geq 11

    First step, subtract three from both sides of the inequality using the rule:

    "An equal quantity may be added to, (or subtracted from) both sides of an inequality without changing the inequality"

    \frac{2}{3}x \geq 8

    Now we have to multiply both sides by 3 using the rule:

    "An equal positive quantity may multiply (or divide) both sides of an inequality without changing the inequality."

    2x \geq 24

    Using the same rule above, we have to divide by 2 to isolate x:

    x \geq 12

    And there you go.

    Another IMPORTANT rule is this:

    "If both sides of an inequality are multiplied (or divided) by a negative quantity then the inequality is reversed"

    I think you can solve the other two.
    Last edited by Aryth; February 11th 2008 at 02:57 PM.
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  3. #3
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    ok, i think i got it, but just to point out.. you only subtracted 2 from the right side, so it would really be (at that point) 2/3x >(=) 8
    thanks
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