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Solve.$$9(2 x+8)=20-(x+5)$$...

Question

Solve.$$9(2 x+8)=20-(x+5)$$

Solve. $$9(2 x+8)=20-(x+5)$$



Answers

Solve. $$9(2 x+8)=20-(x+5)$$

We have to solve the given linear equation to X Last nine is equal to five X. So first we'll bring the light turns together, so we'll bring five. It's on to the left hand side, so that will become two weeks minus five. X last night is equal to zero, which means that minus three X plus nine is equal to zero. Now we'll take of a nine from both sides of the equation. Tau get minus. Tree X is equal to minus nine, and now they divide both sides of the equation with minus tree so that X comes out to be equal to three. So therefore, the solution for the given equation is X is equal to three.

Okay, so we're solving this equation for our variable X, and we can see that we have X plus nine. We need to get X by itself. So let's do the inverse operation of addition, which is subtraction and what we do on one side of the equal sign we have to do on the other. So I plus nine minus nine, cancel out we're left with X. And on the right side of the equal sign, we have not 18 minus nine, which gives us nine. So our final answer is X equals nine.

So we have following 10 into two. X plus four is equal to minus negative eight minus nine x plus three x So let's start distributing here and then solved. So 10 times two x 20 x plus 40 That's equal to minus negative. Eight minus nine x So we have to distribute that negative to both minus eight and minus nine x So that'll be eight plus nine x plus three x. It's combined the like term, so we'll get 20. X Plus 40 is equal to eight plus 12 x. Let's Ah, first start by subtracting 12 x on both sides, so we'll get eight. X plus. 40 is equal to eight now. So eight x plus forties eight. Now let's subtract 40 on both sides. We will get eight. X is equal to minus 32. Now let's divide eight on both sides. We will get eight. Is exes negative for

We're being asked to solve the given equation. Well, to do this, we're going to find are used across products. So first, we're gonna multiply the extremes. So we need to multiply two x times the quantity of nine minus sex. And this will be equal to the product of the means, which are five and X plus four will have five times the quantity of X plus four. So the next we have to do is distribute well. Two x times nine is 18 x and two x times negative x is negative two X square and this will be equal to while five times x is five x and five times four is positive 20. Now, as you can see, we have a quadratic because of that X squared term. So going to set the sequel to zero. So to do that, I'm going to subtract 18 x from both sides as well. Azad two x squared to both sides because then 18 exes and two X squares will cancel, so we're gonna have zero equals. Well, the first term I'm gonna have it's two x squared because it doesn't have a late term. Then I'll come by my exes will five minus 18 is negative. 13 x and then I'll bring down that last term. Positive 20. Okay, so now we want to solve this equation. To do this, I'm going to factor. So because I haven't a term, what we're gonna dio is figure out what's going to multiply two, and I'm gonna multiply a time. See, so two times 20 is equal to 40. So I need to figure out that something's gonna multiply. The 40 foot will add to our middle term Negative 13. So I'm thinking eight and five. And if I let ap negative and five B negative. Negative. Eight times negative. Five is 40 and negative. Eight minus five is negative. 13. So I'm going to replace negative 30 next, when Negative a decks and negative five x. So I'm gonna have zero equals two x squared minus eight X minus five X plus 20. And now I'm gonna faster by grouping. So the GC up for the 1st 2 terms is two x So I have two x times the quantity of X minus four and the GC up for the 2nd 2 terms is negative. Five. Which leaves us with X minus four, which is perfect, because now we have the same ah factor. So when we factor out the X minus four, we have X minus four. An ember left with two X minus five. And now we just have to set both of our factors equal to zero. But as you can see, every another room. So gonna starting new page here. So our first factor was X minus four. We're gonna set that equal to zero. And our second factor was two X minus five. So also set that equal to zero. Now, we just saw both equations, so I'm gonna add for the both sides, so we get X is equal to four. And for the second equation, I'm gonna add five. We get two X equals five, and then we're gonna divide both sides by two. So x will be equal to five house. So we found we have two solutions. X could be four or X. Could be five


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