solve-for-the-variable-and-check-each-solution-is-an-integer-2-x14-3-x10

Question

Solve for the variable and check. Each solution is an integer.
$(2 x+1)+(4-3 x)=10$

M S · Accepted Answer

So first we want to solve for each variable. In this case, we only have X. So we&#x27;re gonna solve for X because we&#x27;re not multiplying anything. He really just dropped thes parentheses, so we&#x27;ll have to It&#x27;s plus one and then plus four minus three X equals two. So now I want to combine like terms when we say combined like times, that means you combine everything, but they must. There variables must have the same degree. So this x of the first and it&#x27;s extra the first we can combine these coefficients. So two minus three is negative one x and in one place for spot. It&#x27;s that they&#x27;re able to 10. So I want to solve like any other allergy problem subject back on both sides. So we have negative X equals. But And if you divide by negative blood on both sides, we get X equals negative by. So when it says check, we want we just want to plug in our X variable into our vision like equation here. So, huh, two times negative by plus one clothes four minus three times later. Bye. I want a stable equals 10 cleverness. So drink. You wanna see but equals 10. So to some, spot was negative. Team close one to have a bee in parentheses. Plus and then we have four and negative three times 85 dozens positive in teams of four plus 15 and negative 10 plus one gives us negative nine and then four plus 15 is 19 and negative. Nine plus 19 gives us tank and tentacles, too, so we know that X equals negative. Five is the correct answer.

M S · Answer

So you want to solve our variable and wanna check So we have for X times exposed to minus X times three plus four x and we won. It&#x27;s equal to X plus 18. So the first thing we need to do is we need to distribute. So for X Times X, we&#x27;re gonna add those exponents. So it&#x27;s our sense of four X squared and then for X times to give us plus eight hits, they would also ate the distribute This negative one accents of this binomial here So negative one times 30 years and negative three. Bring down that X and then negative one x times. For that. You would want some spores negative, for they wanted to add those exponents. Someone plays wise, too. It&#x27;s like that equal into explosive 18. So now we need to combine light terms. That means if they have the same degree, we need to combine the coefficients. So this for X squared here, and it&#x27;s more X squared. Here we can combine their coefficients. The four minus four gives a zero. That means the&#x27;s cancel out because whenever we have zero, the coefficient zero times anything zero. So let&#x27;s just Europe, and these two have and understand Explain it a point. So, eight, Minister, he gives us five X and we&#x27;re gonna set that you consider other side, which is too explicit. 18. So now we need all of our variables on one side and all of our numbers on the other. So I&#x27;m gonna move these two X to the other side. It&#x27;s a non council by minus two is three X and so they got 18 and divide by three on both sides, and we get X equals six. So now we need to plug this back into our original equation to prove that X equal. Six. I just want to check your answer. So you&#x27;re gonna have four times. Six all times. It&#x27;s explicit, too. Minus six times three plus four times six. My shoulders are bigger. Print a sneeze it is. And then to the able to two times six plus 18. So now we just simplify. So four times six is 24 in 66 plus two is eight minus six times three plus and four times 16 24 and equals to some sixes. 12 plus 18. So I&#x27;m going to grab a calculator and 24 times eight. It is 192 money, six terms three plus 24 27 and 12 hours. 18 is 30 someone 92 minus in six times 27 is 162 pernicious 30 and 1 92 minus 1 62 years. I was 30 and because 30 does equal 30 we know that X does equal six.

Cullen Miller · Answer

Hello. I hope you&#x27;re doing well. Server this quadratic equation. First, we&#x27;re going to combine like terms, combining the terms we have 3/4 plus 1/2 X&#x27;s equal to minus 10 straining to get a common denominator between these two. So we can Adams. We&#x27;re gonna have the common denominator of or since equalled. 3/4 waas 2/4 x is equal to minus 10 3/4 plus two ports gives us 5/4. So that&#x27;s 5/4 X is equal to minus time balloon balls by both sides of our equation by 4/5. These cancel out we&#x27;re left with X is equal to minus 40/5, just equal to minus eight. So our solution for this equation is minus eight and this is our final answer here. All right, well, think said, I hope that helps

Amrita Bhasin · Answer

this question asks us to solve each equation and then check her solution. What? We know that the first thing you can do is we can get the 1/5 X and left inside. And then we have negative re over 10 on the right hand side because we brought this term over to the right. We then know that if we divide each term by 10 we have this cause now you&#x27;re putting into the equation. You have negative 1/5 equals negative. One fest. How we did this is acts equals one is our solution, and the one is negative.

Catheryn Taylor · Answer

this question is similar to the previous question where we have to multiply each side of the equation by the least common denominator, which is six. So the least common denominator for two and three s. Six. So we&#x27;re multiplying both of the terms on the left by six. So six times x over two was the same was doing six divided by two. So that gives me three. And I keep the X six times X over three is the same as having six divided by three, which is two. And keep the X And then on the right hand side, I have six times 10 which is 60. Next step, I&#x27;m going to go ahead and combine like terms on the left. So three x plus two X s five x people 60 and then my last step is to divide by five. So 60 divided by five is 12. But I have to check my work before I know that I&#x27;m correct. So anywhere I see X, I&#x27;m going to replace it with 12. So 12 divided by two plus 12 divided by three equals 10 12 divided by two is six 12 divided by three is four and that is in fact 10. So we know that fixes it

Alexia Hamilton · Answer

All right. So we are asked to solve the following equation. And that is five x last three X minus four X equal to 10 plus two. And then we&#x27;re also asked to check our answer to make sure we did everything right. So win solving equations and you&#x27;ve got, like, terms on the same side. You need Teoh. Well, the first step is to simplify the individual sides the left side on the right side of the equal sign. So for this problem, when simplifying the left hand side, we are combining like terms because I have the five x three x in the forex. So they all have the same form of the variable X. They&#x27;re all just X. Is there not, like X squared or anything? They&#x27;re all the same type of an ex, so they&#x27;re all like terms so I can combine them. So I&#x27;m just going to do the order of operations. I&#x27;m going to start on the left and work my way to the right, So five x plus three x is eight X and then I&#x27;m also going to combine my leg terms on the right hand side. So 10 in two are also like turns because neither of them have the variable X so they can be combined. So 10 plus two is a 12. All right, so the right hand side is simplified. The left hand side still needs a little bit of work, cause I haven&#x27;t eight x minus of four x will eight x minus four x their like terms they can be combined and that gives us a four X equal to 12. And then I get to solve for my variable X. When you&#x27;re solving for the variable you want toe, isolate it. So I want to get X by itself. Right now it&#x27;s being multiplied by four. So if I need so I need to move the four away. And the way that we move the four away from the variable is by doing the opposite of the operation. So the opposite operations of multiplication is division. So I need a divide by four on the left hand side, and I have to also divide by four on the right hand side. Because algebra is a balancing act and what you do, the one side you have to do to the other side of unequal sign So I&#x27;m dividing by four in both sides. That leaves me with just a X because four divided by four is one. And mathematicians don&#x27;t write invisible ones in front of variables equal to 12 divided by four is three. All right, so now I think my answer is or my solution for the equation is X equal to three. Now, I have to check my answer. So I&#x27;m gonna go back to my original equation a five x plus three that&#x27;s minus four X equal to 10 plus two. And wherever I see in X, I&#x27;m going to replace it with the number that I think is my solution. So all three of those exes there&#x27;s gonna be replaced by three. So that&#x27;s a five times three plus a three times three minus a four times three equal to 10 plus trip. And then I kind of go through again and simplify both sides of the equal scientists, but only, but I&#x27;m Onley simplifying. I&#x27;m not moving sides around. So, using the order of operations, I need to do multiplication or division first from left to right. So I&#x27;m gonna just kind of do all of my multiplication, so I have a multiplication here of five times three. That&#x27;s 15. Three times three is nine. That plus in just gets brought down. Gonna go ahead and bring down that minus sign and then four times three is 12. Or you can think of it as a negative Ford Times a positive three, which gives you a negative 12 equal to There&#x27;s no multiplication on the right hand side. So I&#x27;m just going to rewrite the 10 plus two, all right? And now we have addition and subtraction left in our problem and the kid that can be done simultaneously left to right. But I&#x27;m just gonna go ahead and do one at a time. So 15 plus nine is 24 minus 12 and then because I&#x27;m moving over to the other side, I&#x27;m gonna go ahead and do that edition as well. 10 plus two is 12 and then lastly, 24 minus 12 is 12 equal to 12. So the way we know that our solution or the number that we think is the solution to the number that we put in place of all of the exes is in fact, the correct solution is when you get a true statement. Like what we have here. When a number 12 is equal to itself, you get a true statement, which means that that value

Problem

Solve for the variable and check. Each solution i…

Problem 24 Medium Difficulty

Solve for the variable and check. Each solution is an integer.
$(2 x+1)+(4-3 x)=10$

Answer

$I=-5$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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Absolute Value - Example 1

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$I=-5$

Algebra 2 and Trigonometry

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Absolute Value - Example 1

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Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Heather Z.

Caleb E.

Maria G.

Ann Xavier Gantert

Algebra 2 and Trigonometry