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Math Help - 1st post from a math noob who is completely clueless...

  1. #1
    videodrome
    Guest

    1st post from a math noob who is completely clueless...

    hello. i recently returned to school after dealing with the flu and im way behind. I got some work out of the book today and im clueless as to how to even go about deciphering what evaluate and simplify means. heres the problems i need to work on.

    1. 3x - 2 (x+5)
    2. 4(a - 3b) - (5a - b)
    3. 2x - 3[ x - 4 (2-x)]
    4. -4[4y-3(y-2)]
    5. -2[x - 2(x-y)] + 5y
    6. 5[2-3(6x-1)]
    7. -2(4xsquared - 5)
    8. -9(-y squared + 4y-1)
    9. - 1/2 (-2x)
    10. 44x(1/11)
    11. 7x+(-11y)+9x
    12. 9a+2b-(-6a)+7b

    evaluate the following
    1. 5a-3b squared when a=-6 and b= 2
    2. a-4b/2c when a=1 b=-1 and c=5

    would somebody be so kind as to tell me what simplifying and evaluating mean in this context and a simple dummy-proof formula/protocol that i can apply to all these so i can solve them myself. im one that learns from example so if someone could solve a few of these with the essential steps needed id really really appreciate it.thanks.
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  2. #2
    Newbie
    Joined
    Nov 2007
    Posts
    18
    Quote Originally Posted by videodrome View Post
    hello. i recently returned to school after dealing with the flu and im way behind. I got some work out of the book today and im clueless as to how to even go about deciphering what evaluate and simplify means. heres the problems i need to work on.

    1. 3x - 2 (x+5)
    2. 4(a - 3b) - (5a - b)
    3. 2x - 3[ x - 4 (2-x)]
    4. -4[4y-3(y-2)]
    5. -2[x - 2(x-y)] + 5y
    6. 5[2-3(6x-1)]
    7. -2(4xsquared - 5)
    8. -9(-y squared + 4y-1)
    9. - 1/2 (-2x)
    10. 44x(1/11)
    11. 7x+(-11y)+9x
    12. 9a+2b-(-6a)+7b

    evaluate the following
    1. 5a-3b squared when a=-6 and b= 2
    2. a-4b/2c when a=1 b=-1 and c=5

    would somebody be so kind as to tell me what simplifying and evaluating mean in this context and a simple dummy-proof formula/protocol that i can apply to all these so i can solve them myself. im one that learns from example so if someone could solve a few of these with the essential steps needed id really really appreciate it.thanks.
    Since you didn't say, im guessing the first cluster of questions asks to "simplify", and as you wrote the second asks to "evaluate"... the way I think about it is simplify means: put into lowest terms possible, or get as close to the answer as you can. This applies to expressions, and anything with unknowns, since we cannot solve it completely. Evaluating, like those examples you gave, is when the unknowns are given to you and you must find an answer.

    So, number 1)

    3x - 2 (x+5)

    When you have a number infront of brackets, you must multiple the brackets out, meaning: multiple the 2 by the x, then multiply the 2 by the 5. I don't exactly know how much you've learned about solving this, so im assuming you know BEDMAS. That's why we need to get rid of brakets first before doing anything else. This gives us:

    3x - 2x - 10 (remember to keep track of you signs +/-)
    x - 10 is your simplified answer.

    4. -4[4y-3(y-2)]

    When you have (4y - 3)(y - 2) you have to multiply the 4y by the y, then by the -2. Then multiply the -3 by the y, then by the -2.
    (4y^2 means it is squared) This gives you:

    -4 (4y^2 - 8y - 3y + 6)

    Now you multiply the -4 by everything inside the brakets.

    -16y^2 + 32y + 12y - 20

    Collect like terms:

    -16y^2 + 44y - 20

    And that's your simplified answer.

    Hope these two examples gives you an idea as to how you go about simplifying. For evaluating, all you have to do is sub in the value of the unknowns given to you into the expression and solve:

    1. 5a-3b squared when a=-6 and b= 2

    5(-6) - 3(2)
    -30 - 6
    -36 is your answer.

    Hope that helped! Perhaps someone can further explain it better then myself if you still have questions
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  3. #3
    Newbie
    Joined
    Oct 2007
    Posts
    14
    When they say "simplify" it basically means "make it look pretty".
    They want you to collect the terms so that a given variable only shows up one time. For example, to simplify 2x + x + 2b -b I would just collect the terms to get 3x + b.

    When they say "evaluate" it just means plug in the given value for the given variable. For example if you were asked to evaluate
    3x + b at x = 1 and b = 2,
    you would just plug in 1 for x and 2 for b in the equation 3x + b to get
    3(1) + (2) = 3 + 2 = 5

    Some general rules of algebra that are useful for simplifying:
    1. x(A + B) = xA + xB -- for example 5(3 + 2) = 5(3) + 5(2)
    -- this rule can be applied from right to left as well
    -- for example: 2x + 3x = (2 + 3)x = 5x
    2. x(A/B) = (xA)/B -- for example 3(2/6) = (3*2)/6

    also, when using rule 1, if x is a negative number remember to multiply both A and B by the negative.

    For example, problem #3:
    2x - 3[ x - 4 (2-x)]
    --usually you want to start from the inside and work you way out, it just makes the math easier in my opinion

    so, the first thing would be to apply rule 1 to -4(2-x) to get: (-4)2 - (-4)x = -8 + x
    So, the current equation is: 2x - 3[ x - 8 + x]

    then we apply rule 1 to -3[ x - 8 + x] to get: (-3)x - (-3)8 + (-3)x = -3x + 24 -3x
    So the current equation is: 2x -3x + 24 -3x
    Then we "collect like terms" (aka use rule 1 from right to left) to get:
    (2 -3 -3)x + 24 = -4x + 24
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