Distributive property [FONT=Verdana, Arial, Helvetica, sans-serif]The distributive property comes into play when an expression involves both addition and multiplication. A longer name for it is, "the distributive property of multiplication over addition." It tells us that if a term is multiplied by terms in parenthesis, we need to "distribute" the multiplication over all the terms inside.[/FONT] [FONT=Verdana, Arial, Helvetica, sans-serif][SIZE=-1]2x(5 + y) = 10x + 2xy [/SIZE][/FONT][SIZE=-1]Even though order of operations says that you must add the terms inside the parenthesis first, the distributive property allows you to simplify the expression by multiplying every term inside the parenthesis by the multiplier. This simplifies the expression.[/SIZE] http://www.math.com/school/subject2/lessons/S2U2L1DP.html
The key take away from your example sound be each term was multiplied by 2x, not just x by itself. Similarly, if it were, say... 2/x, you would have had to bring 2/x along for the ride just like you did for 2x. You COULD argue that either x or 2 could go in since multiplication is commutative, but that would miss the point of the example and render it irrelevant to this thread. It gets a lot more obvious when you start working through samples that aren't ONLY multiplication and addition... You can find more examples of that in the link I posted earlier where I said to pay particular attention to what happens when there is more than one term outside the parenthesis. There is a reason you won't find one that only "distributes" one of many terms that existed right next to each other on the same order outside the parens.
I used that in this case so 7/4x=2(5+3) is how this is written correct. So simple answer is unsolvable then because it breaks down to 28. 7/4x=16 7*7/4x=16*7 4x=112 4/4x=112/4 x=28
Here's where you went wrong: 7/4x = 16 7*(7/4x) = 16 * 7 You can't just tack a non-commutative operation onto whatever term is convenient. It has to apply to the ENTIRE side of the equation, or nothing at all...
ok well mine doesnt and yours does so I'll believe ya on this one but the last one is still 288 lol. Like I said it's been 7 years since I've done this stuff.
I'm surprised that no one has commented on my words. But anyway, I can still 'add' to this debate, lol. The distributive property still applies here, watch! 48÷2(9+3) = (48/2)*9 + (48/2)*3 = 288 Do you all see how the distributive property works now? Also, I have to disagree with what people are saying about how the equation is written. There is nothing wrong with the way it is written. When you have the capability to write in muli-line or "pretty print" it simply makes it easier to see what is happening. 48 ----(9+3) = 48÷2(9+3) = 288 2 48 ------ = 48÷(2(9+3)) = 2 2(9+3) Hope that helps! ~Dan
The "and" in the phrase "2 and three quarters" does not mean multiply. It means add. What you wrote is multiplication. You're really reaching now. If anyone ever writes (2*3/4) when attempting to represent 2.75, punch them in the mouth on general principle. perhaps scream something about the distributive property not applying while you're at it. Keep 'em guessing.
At this point I think you're just getting trolled. I also found this article on why the TI-85 gives implied multiplication a higher priority. They also admit that it's technically wrong and it's just done to save time when entering the equation. http://epsstore.ti.com/OA_HTML/csksxvm.jsp?nSetId=103110
I'm not sure I'd call it 'my way'. I could've solved it ten different ways but what matters is that my answer is correct.
my head hurts... also I still wanna see that plane take off!! (ill stand on the ground to watch though)
