Answered

CANT get these WRONG. EXPLANATION WOULD BE NICE. if you can

  1. What is the perimeter of a triangle with the given side lengths?

s1 = 2x + 1 cm

s2 = 3x + 2 cm

s3 = x + 3 cm

p = ?x + ? cm


  1. A teacher wrote expressions on cards and put them in a bag. Thomas and Kelly drew cards from the bag and added the expressions. Thomas drew 3x + 7 and 2x - 3. Kelly drew the expressions -6x + 3 and 14x + 2. How much greater was Kelly's sum than Thomas's sum?

?x + ?

Verified Answer :

  1. To figure out the perimeter of a triangle, you need to add all of the side lengths together. 
    =(2x+1)+(3x+2)+(x+3)
    Because there is no multiplication, you can remove the brackets separating the terms.
    =2x+1+3x+2+x+3
    The next step is to rearrange the expression so that like terms (terms with the same variable) are grouped together. 
    =x+2x+3x+1+2+3
    Then, you can add together the terms that have like terms.
    =6x+6
    Always add a therefore statement at the end of your solution for full marks.
    ∴ the perimeter of the triangle is 6x+6

    2. The first step is to figure out what you need to do. For this equation, you need to figure out the difference between the sum of the first two expressions and the sum of the last two.
    T=(3x+7)+(2x-3)
    K=(-6x+3)+(14x+2)
    To find out the difference, you must subtract one expression from the others. Because the question indicates that Kelly had the greater sum, we will subtract Thomas's sum from Kelly's.
    K-T
    =[(-6x+3)+(14x+2)]-[(3x+7)+(2x-3)]
    Make sure to put Thomas's whole expression in another set of brackets, otherwise you will not get the right solution.
    Next, simplify what is in the brackets.
    =(    -6x+3+14x+2)-(3x+7+2x-3)
    Next, group like terms.
    =(14x-6x+3+2)-(2x+3x+7-3)
    Then, add together like terms.
    =(8x+5)-(3x+4)
    Multiple each term in the second bracket by -1, because it is being subtracted.
    =8x+5-3x-4
    Group like terms.
    =8x-3x+5-4
    Add like terms.
    =5x+1
    ∴Kelly's sum was 5x+1 units greater than Thomas's.

#1 is actually 3+ 3ft and #2 is actually 3x+1



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