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For what values of x the expressionY3x? +4 -4 Is subject to subtractive cancellation and how can be evaluated more accurarely to avoid the problem?...

Question

For what values of x the expressionY3x? +4 -4 Is subject to subtractive cancellation and how can be evaluated more accurarely to avoid the problem?

For what values of x the expression Y3x? +4 -4 Is subject to subtractive cancellation and how can be evaluated more accurarely to avoid the problem?



Answers

Identify the following as either an expression or an equation. $$x-4+5 x$$

We've been told to sit five X plus or equal to zero. And then so Rex. So the first thing they told us was to set this expression equal to zero. So all that means is we're gonna take this expression, and we're going to say that it is equal to zero. So now we have an equation. So all we have to do is move things around and get X all by itself on one side of the equation. So it's on the left right now, So I'm just going to start by moving things over from the ex. The two things that are with the X on the left side are this five and this four before is attached to the X through addition. It's just being added on the bar is attached to the multiplication. So what I would do first is to attract before, because that will be It won't make things, ms, because the truck for on one side of the equation, I have to do it to the other side because then I can keep things equal. You can always think about equations as like a balance scale. If you do something, if you put something or take something off one side of the scale. You have to do the exact same thing on the other side. Otherwise you won't balanced anymore. So I'm distracting for from both sides. So on the left side, my plus four and minus four cancel, which is exactly what we wanted. And then we're left with five times X on the left side. On the right side of the equation, we have zero minus four, and that gives us negative for so now, the only thing we have to get rid of is the five, and then X will be all by itself. So since it's being multiplied to the X to get rid of that, I I'm going to divide by five. So again I'm dividing by five on one side of the equation. I have to do the same thing to the other side to keep everything balanced. So on the left side, the five divided by five cancels and we're just left with X. So excess finally love. And then on the right side, we have negative or bits. If you wanted to, you could turn this into a decimal by, um hugging, negative or divided by five in your calculator. But we're just gonna leave this as a fraction because it's less work. So we get X equals negative forfeits.

For this problem that you will use the least common denominator to be able to solve for X. To start, you notice that there is one X on the left side of the equation while there is two X. Is on the right side. So you will want to multiply the four of her X times two as you can get the same denominator. This will equal eight over two X minus two. Equalling 2 5/2 X. Since the exes are both in the denominator, you know the X cannot equal zero. The next step will be to add to the both sides on the left side. They will cross out because they equal to zero and then add it to the right. This will equal yeah 8/2 X. Equalling 2, 5/2, X plus two. Now that both of the denominators are the same, you are able to combine the like terms to do this, you will subtract 5/2 X on both sides. On the right side of the problem, they will cross out an equal zero while on the left side. You are able to just subtract the numerator since they have the same denominators, this will equal to three over two X. Equalling two. Now that the exes are combined, you are able to get X out of the denominator to do this, you can multiply both sides by two X. On the left side. They cross out because there's one in the numerator and one of the denominator. And then on the right side of the problem they will just be multiplied by two. So this will equal three equals four X. The very last step will be to get X by itself to do this, you can divide both sides by four. On the right side of the problem, the fours will cancel out because they equal the one so X. Well equal 3/4

Okay. So to figure out what we have to add to negative four acts to be zero. So I'm gonna making equation negative four x So whatever we add to negative work. So let's make that be why. And then we want this some to be a zero. So we'll return to solve is why so from here, I can add for extra bolt sides. So this will tell me that our term that we need to add to negative four acts is going to be positive for X. So this makes sense. Because if we write it now like this negative four x plus positive for X does equal zero cause these cancel out. So our answer is going to be four x.

Today we are doing polynomial and rational inequalities. Here, we are given the expression for x minus three over X plus one Equals zero, and we are asked to determine what the values of X. The expression is undefined. The expression is undefined whatever the denominator equal zero, So we're going to take that denominator of X plus one and set it equal to zero, solving for X. We subtract one from both sides and we're left with X equals negative one, so for X equals negative one, the expression will be undefined.


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