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Equations2018-07-06T13:18:16+10:00

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    Keymaster
    July 6, 2018 at 1:18 pm
    Post count: 1622
    #13902

    Solve $$\frac{x-10}{2}=6$$.

    $$\frac{x-10}{\cancel{2}}^{\cancel{\times2}}=6^{\times2}$$     multiply both sides by 2

    x – 10 = 12   add 10 to both sides

    x = 22

    Admin
    Keymaster
    July 6, 2018 at 1:21 pm
    Post count: 1622
    #13904
     Solve 12500 = 36500(1 – r)³ for r.

    $$\frac{12500}{36500}=(1-r)^3$$

    $$\frac{25}{73}=(1-r)^3$$

    divide both sides by 36,500

     
    $$\sqrt[3]{\frac{25}{73}}=1-r$$ take the cube root of both sides, cancelling the cube on the right
    $$\sqrt[3]{\frac{25}{73}}+r=1$$ add r to both sides
    $$r=1-\sqrt[3]{\frac{25}{73}}$$ subtract $$\sqrt[3]{\frac{25}{73}}$$ from both sides
    r = 0.3 calculate
    Admin
    Keymaster
    November 29, 2018 at 9:30 am
    Post count: 1622
    #14783

    If X = 2a + b and Y = a – b, then find the value of a + 2b.

    (X = 2a + b)  – (Y = a – b)

    X – Y = 2a – a + b – -b

    X – Y = a + 2b

    ∴ a + 2b = X – Y

    Admin
    Keymaster
    November 29, 2018 at 9:32 am
    Post count: 1622
    #14784

    The sum of three consecutive even numbers is 84. If the middle number is 2x + 4, what is the value of x?

    consecutive means in a row so the one before it would be: (2x + 4) – 1 = 2x + 3
    the one after it would be (2x + 4) + 1 = 2x + 5
    first number: 2x + 3 middle number: 2x + 4 last number: 2x + 5   
    2x + 3 + 2x + 4 + 2x + 5 = 84
    6x + 12 = 84 
    6x = 72 
    x = 12 

    Admin
    Keymaster
    January 1, 2021 at 1:29 pm
    Post count: 1622
    #18949
    If 1.05x  = 2. Find the value of x.

    x = 2
    1.052 = 1.1025 

    		 Method 1: Guess and Check you start with any number and check, then modify the next guess until you get close to the answer

    1.0510 = 1.62
    1.0520 = 2.65
    1.0515 = 2.07
    1.0514 = 1.97
    1.0514.5 = 2.02
    1.0514.2 = 1.999
    ∴ x = 14.2

     

    Start with any number. We are starting with x = 2
    Calculate and see how close you are to the answer you want
    since it is too small, try a bigger number, say x = 10, which brings us closer to the answer, but we are still too small
    x = 20 was too big, so we now know it is between 10 and 20.
    Keep trying and refine your estimate until you get to the answer

    $$x=\frac{log\;2}{log\;1.05}$$

    x = 14.2

    		 Method 2: Using logs you don’t have to understand the log here, just follow the rule and memorise it. This is a more advanced method, but will always work for these types of equations if you can just remember which one is on top and which one is on the bottom
    x= log the answer part (2) divided by log the question part (1.05)
    Admin
    Keymaster
    January 1, 2021 at 1:30 pm
    Post count: 1622
    #18950

    Solve for x: ##\frac{{3x}}{4} – 5 = \frac{x}{5} + \frac{1}{2}##
    ##^{\times\cancel4\times5\times2}\frac{{3x}}{\cancel4} – 5^{\times4\times5\times2} = \frac{x}{\cancel5}^{\times4\times\cancel5\times2} + \frac{1}{\cancel2}^{\times4\times5\times\cancel2}## multiply everything by 4, 5 and 2

    30x – 200 = 8x + 20

    		 simplify

    22x – 200 = 20

    		 subtract 8x from both sides

    22x = 220

    		 add 200 to both sides
    x = 10 divide both sides by 22
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