5

13 Solve thematrx equations:85 774(39 Tar #FX ^(J(J 43 ^(J 6 IR A3...

Question

13 Solve thematrx equations:85 774(39 Tar #FX ^(J(J 43 ^(J 6 IR A3

13 Solve thematrx equations: 85 77 4(39 Tar #FX ^(J(J 43 ^(J 6 IR A3



Answers

Solve the equations for the variable.
$$5.6 r+13.1=3.5 r+57.2$$

Okay. Problem. 13. We are still solving for X. We got X over seven equals 13. I want to go ahead and be right that first we got X over seven egos. 13. Okay, so I want to isolate X on the left side. Right? And the way we want to do that, since X is divided by seven, I wanna cancel that seven by multiplying this some term by seven. Okay. I want to bite by seven. And since I'm multiplying the left side by seven, I need to do the same thing on. So for me, I mean, multiply this by seven and do the same thing for 13. Okay, so now both sides are multiplied by seven, so we're not changing the value of X. So, um, you got seven here, and one essentially won over seven. So those those things cancel. Right? So we're left with X, and we got 13 times seven, and that's perform our multiplication on the right side about 13 times 77 times three is to anyone. So where I want and care be over to seven times one of seven less to is nine. We got 91. So acts equals 91

Yeah. The first thing we have to do to solve this equation is to get our variables on the same side. So we're gonna pick the variable that has the smaller coefficient in this case 3.5 is smaller than 5.6. And we're gonna move that term to the other side of the equation. Since this is a positive 3.5 are we're going to have to subtract 3.5 are on both sides. So when we do that that gives us 2.1 are? Yeah. Mhm. Plus 13.1 Yeah equals 57.2. Mhm. So now that we have our variables on the same side, we need to get our constant terms on the same side which means we're going to need to move this 13.1. So the 13.1 is being added. So we're going to subtract 13.1 from both sides. And that gives us 2.1 R equals 44 0.1 when we subtract those numbers. And then finally the last thing we need to do to get the are by itself the R. Is currently being multiplied by 2.1. So to undo that we need to divide by 2.1 on both sides. And when we divide by 2.1 we get our equals 21. So now we have to check our answer to do that. We're going to go back to the original equation from the beginning of the problem. Mhm. And we're going to plug in the 21 that we got that's going to go in for both of the our terms in this equation. Mhm. Mhm. So when we plug that in we'll have 5.6 times 21 plus 13.1 equals 3.5 times 21 plus 57.2. So now we just need to um perform these operations, evaluate on each side of the equal sign. So we'll start with the multiplication 5.6 times 21 is 1 17.6 plus 13.1 and then 3.5 times 21 is 73 0.5 plus 57.2. And then the last step is just to add the numbers on each side. So on the left, when we add those together, we get 1 30.7 and on the right when we add those together, we also get 1 30.7. So since we have the same number on both sides of the equal sign, that means that our equation checks out. So our answer is correct. So our original answer of R equals 21 is the correct solution for this equation. Mhm.

In order to solve this equation. The first thing we have to do is get our variables on the same side. So we're going to take the variable term with the smaller coefficient and move it to the other side of the equation. So our two variable terms are seven X. And negative Adex. The smaller of those is negative Adex. So that's the term that we're going to be moving Since it's a -8 x. In order to move it we're going to add a positive eight X to both sides of the equation. Mhm. Once we've done that we can combine our like terms seven X plus eight X. Gives us 15 X minus 17 equals 13 From there. We still need to isolate our variable. So we've got the 17 that's being subtracted from the X. Since it's being subtracted, we're gonna add 17 to both sides And that leaves us with 15 x equals 30. And then finally the X. is being multiplied by 15. So to get rid of that we're gonna divide by 15 on both sides. And that will cancel out and give us X equals two when we divide that. Yeah. So now we just need to check our answer and verify that it is in fact correct. So to do that we're going to go back to the original equation and we're gonna take this to that. We just got and we're gonna plug it in for each of the X. Is in the equation. So when we plug that in we're going to have seven times two minus 17 Equals -8 times two plus 13. So now we just need to simplify these by performing these operations. So we'll start with the multiplication seven times 2 is 14 minus 17 and negative eight times two is negative 16 Plus 13. And then we'll just combine the terms on each side. 14 -17 is negative three, negative 16 plus 13 is also negative three. Since we got the same number on both sides of the equation, that means our answer checks out. So our original solution x equals two, is the correct final solution for this equation.

We need to solve the following equation, so we're going to move the M from the right side to the left side, So we're left with 3 -1 is two. M minus seven equals negative 13. R. M. S on the right side, cancel each other out. We add 7 to both sides. Can we get to em Our 7s cancel out is equal to -6. We divide both sides by two, And we get em is equal to -3.


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