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1.(32pts) Solve the following dlillereutial ,juations...

Question

1.(32pts) Solve the following dlillereutial ,juations

1.(32pts) Solve the following dlillereutial ,juations



Answers

Solve each equation using the steps outlined in the text. $$6 u-5-8 u=-7$$

Right problem. 27 were asked to solve an absolutely equation. Ah, here. We haven't ate that sitting outside of the absolute value, but it's on the same side of the equation with the observation. So we have to give his efforts. So gonna divide both sides by eight. To get rid of that, it's eight times and the opposite of modifications division. Once we do that we have w minus seven equals nine. Once you have the absolute value, isolated now could do the rewrite. So we write W minus seven equals nine. And of you minus seven equals negative. Not right. We leave the inside alone. And we changed the nine to positive and negative versions. All right? And we had seven to both sides and a vehicle 16. That's in the both sides. And we get Debbie was too. Now, some of you might think so, but I didn't do that isolated. I didn't isolate the absolute, and I still got the same answer. Well, sometimes that works. So in this problem, it turns out that okay, but don't count on. So usually so get in the habit of isolating the absolute I first. Now let's check our solutions. So when a substituted into the original operations of eight times 16 minus seven, is that equal 72? So 16 minus seven is not. Does that equal sent me to Absolutely nine is nine and a timeline. They sent me to sew you up. That worked. Let's check the other one. Negative to minus seven. Is Daddy with 72? So eight times never to minus seven is negative. Nine. After that, an alien I miss positive nine and again Eight times nine sent me to. So that worked. So both answers work. Giving us the answer's negative, too. And 16 that's it.

Here we have an equation to solve and solving. It means to isolate X so we can find the value of X. So the first thing we would do to both sides is subtract ified. And that's because of the subtraction property of equality. And now we have eight. X equals 56. The next thing we want to do to get rid of the multiplying by eight is to divide by eight. And that's because of the division property of equality. And now we have X equals seven.

Okay, so we want to salt the falling for X. Well, this is already in fact it for so we have to Solution X minus six is equal to zero and two x plus wanted you because they're all solving for X. We get X is equal to six, an acceptable to a negative 1/2.

We're looking at mm and were justified when the function of X equals x minus two. Provided. Uh huh. This function is greater than zero. So what this means is that this fraction here is positive. Now it's happened when the numerator and denominator are both positive. But when the numerator and denominator both negative. So case one and the pope positive. This means X -2 is greater than zero and party an ex possible great terms error. Now what leaves me is that grateful vera The next is greater than -4. Russia being too sorry. And so the only way for both of these equalities to be true at the same time is bull okay to be great them too because he's gracing them to greater than mine as well. So we can see the house the both negative the wrecks man is two is less than zero. Next passport There's less than zero. And what these mean If X is less than two annex less than mine is full. So believe to be true the most powerful act Less than -4 Because it's less than 94. It will also be less than two Nazi anyway for these two or cold self be true. Same time your solution. Hear that Grace and zero birthday Is greater than two. Okay. Is less than -4 where we can write this as right interval From Minour Infinity -4 unions. Two her in Tennessee.


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