x + 1 over 3 = 1/5 Solve the PROPORTION for x - AVOID This COMMON ALGEBRA MISTAKE!
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- เผยแพร่เมื่อ 23 ก.ย. 2024
- How to solve a proportion in algebra using the cross product. Learn more math at TCMathAcademy.....
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No paper needed: x + 1 = 3/5 so x = 3/5 - 5/5 = - 2/5
Absolutely correct. No paper needed. Solved it in about 3 seconds.
It occurs to me that this is a good place to share something i was explaining to a friend's grandchild a while back. Because apparently some people have trouble visualising it. The easy way to subtract x from y when both are positive but x is greater than y. Ie, when we can see the result will be negative.
Formally, I'd say it like this:
If x > y then
y − x = −(x − y)
Informally: Subtract the smaller from the larger and stick a negative sign in front of the result.
So, for instance, 17 − 20
= −(20 − 17)
= −3
Or in the pertinent part of the problem in the video:
⅗ − 1
= −(1 − ⅗)
= −⅖
Not the greatest insight in the world, I realise, but it might help somebody.
(X + 1)/3 = 1/5
Invert both sides
3/(x+1)=5
3=5x+5
5x=-2
x=-2/5
@tomtke7351 You forgot the minus sign in front the 2 to the right side of the 5x.
Why wouldn’t you multiply both sides by 3 and the solve for X? That seems the simplest method.(for me)
I agree.
But even if you are going to multiply both sides by 5 as well, to get 5(x+1)=3, and then solve it from there, it's completely unnecessary to couch it in terminology like "proportion" and "cross product".
We are just multiplying both sides of an equation by the same factor. It's standard, normal, routine equation manipulation. It doesn't need a special name because there's nothing special about it.
I needed the full explanation.
(X + 1)/3 = 1/5
multiply both sides by 15
15(x+1)/3=15(1)/5
5x + 5 = 3
5x = -2
Divide both sides by 5
x = (-2/5)
VERIFY
(X + 1)/3 = 1/5
with x = (-2/5)
((-2/5)+1)/3=?(1/5)
((-2/5)+(5/5))/3=?(1/5)
(3/5)/3=?(1/5]
1/5=❤1/5✔️
(x + 1)/3 = 1/5 The LCD of 3 and 5 is 15
5(x + 1)/15 = 3/15 both sides are /15 so ....
5(x + 1) = 3
5x + 5 = 3 subtract 5 from both sides
5x = - 2 divide both sides by 5
x = - 2 / 5
Cross multiplying,
5(X+1)=3
5X+5=3
5X= 3-5=-2
X= -2/5
If we put x = -0.4 we will balance the proportion.
-0.4+1 will be x = 0.6 that is what we need.
Or 3x1/5=0.6
0.6-1=-0.4 or -2/5
At thuail, in head, ~20 seconds, yadda yadda, the answer is -2/5.
Starting with:
(x + 1) / 3 = 1 / 5
Multiply both sides by 3 to get:
x + 1 = 3 / 5
Subtract 1 from both sides to get:
x = 3/5 - 5/5 = -2/5
I also used this method, also on my head in a few seconds. Were we taught differently? I finished school in 1969
(x + 1/3) = 1/5
5x + 5 = 3
5x = -2
x = -2/5
[x + 1] / [3] = 1/5
3 * [x + 1] / [3] = [1/5 ] * 3
x + 1 = 3/5 x = [3/5] - 1 ### 1 = 5/5 ### x = [3/5] - [5/5] x = -2/5
proof by substitution ----> [-[2/5] + 1] / [3] = [3/5] / [3] = [3/5] * [1/3] = 3/15 = 1/5
ANS:: -2/5
He's right. The first thing to do is cross multiply:
(x+1)/3 = 1/5
5x+5 = 3
5x = 3-5
x = (3-5)/5
x = -2/5
He's not right. He's massively over-complicating it.
Multiply each side by three. x + 1 = 3/5
Subtract one from each side. x = −2/5
Job done, in two simple steps.
"Cross multiply" is a fancy way of saying multiply both sides by 15.
It's perfectly valid to do that, but it seems a bit pointless when almost immediately afterwards you're going to divide both sides by 5.
Elsie Dee, Elsie Dee, Elsie Dee ! (HEY! If you can do "Please Excuse My Dear Aunt Sally", I can do "Elsie Dee".)
Means-extremes products property of a proportion.
why did you make it more complicated then it needed to be? JUST SOLVE FOR X!!!!!!!!!!!!!!!!!!
Step 1: Isolate the x + 1 by multiplying both sides by 3.
Gives us x + 1 = 3/5
Step 2: Isolate the x by subtracting 1 from both sides
Gives us x = 3/5 -1 or x = 3/5 - 5/5 which is the final answer -2/5
Super easy, doesn't need 12 minutes to explain or a click bait title that makes you think the question isn't asking for the value of x.
I needed paper, but got .2
got -2/5 thanks for the fun.
why do they time each problem in jr college for example like this video in school they give me 1 min. to answer it if you go over 1 min they mark it wrong
I have the same complaint. That's why I hate hiring people right out of school. They're trained to prioritize speed over accuracy - "Answer all of the questions quickly, then go back and check your work". They're never taught, "make sure you get the right answer no matter how long it takes". And they're rarely trained on how to verify their work.
-2/5
x = -2/5
X = -2/5 or
X = -.40
Your solutionseems a bit to complicated to me. Why not multiply both sides with 3 to get
X+1=3/5
Subtract 1 from both sides and there you are
Blimey that's an odd way of doing it. Just multiply both sides by 3.
(x + 1)⁄3 = ⅕
x + 1 = ⅗
x = −⅖
-2/5
X=-2/5
-2/5
-2/5
X= - 2/5
Lowercase x so x = - 2/5 but I love the space between the minus sign and 2/5 you put there.