solve-for-the-variable-and-check-each-solution-is-an-integer-3-a7-a-114

Question

Solve for the variable and check. Each solution is an integer.
$(3 a+7)-(a-1)=14$

Aditya Sood · Accepted Answer

welcome. We&#x27;re going to be solving for a in this equation. And so the question we&#x27;re giving us three a minus seven minus a minus one is 0 to 14. Our first step is going to be to distribute this negative sign. So we get 3897 minus a negative, and a negative makes a positive. So get a plus one is equal to 14 will combine like firms. So three a minus a is to a and negative seven plus one is negative. Six is equal to 14. Add six to both sides to get to a is equal to 20 and divide both sides by two. And so to a divided by two is a and 20 divided by two is 10. So our answer is A is equal to 10. But there&#x27;s more of that this problem because it wants us to check our work. And so the way we could check our work is by substituting this value of a 0 to 10 right back into this equation on dhe. Um, and if we substituted into this equation and get off the value of 14 we know that is indeed equal to 10. Otherwise, we know we&#x27;ve made an error somewhere, so let&#x27;s substitute this. So three times 10 minus seven, minus 10 minus one. And so this is pretty much just where they used to be. And now there&#x27;s 10 because that&#x27;s the value we found for it. We&#x27;ll evaluate this further, to get 30 minus seven minus 10 minus one, which is the same thing as 23 minus nine. Uh, 23 minus nine is indeed 14 and 14 is also the value that we were actually looking for. And so now we know that a is indeed equal 10 and we&#x27;ve checked our work.

M S · Answer

in this problem we want to solve with variable in check. So first, let&#x27;s solve for our variable. So I&#x27;m gonna distribute this to into our binomial 17 times be used to be in two times negative three&#x27;s negative six and then we won&#x27;t distribute This three said three times be is three d. M. Three times four is 12 and no equal B plus 14 So now is simplify and by combining like terms so this b and this be both haven&#x27;t exploded of one. That means we can combine nickel efficient. So two plus three is five and emotions speed in 12 months, six and sticks and so they wouldn&#x27;t be plus 14. So now we want all of our variables on one side and all our numbers on the other. So unless attract, be from both sides. So that&#x27;ll council over here, Bob on his one is four. And then I want this six on the other side. So subtract sticks on both sides. Well, there are four b equals eight and if you divide by four on both sides, we get B equals two. So now that we know the equals two, we need to play this back into our equation and see if the one side equals the other. So we have two times two minus three plus bring times two plus four and hopefully that unequal to plus 14. The two times T minus three is negative point and two plus 46 in two plus 14 16 two times negative points. Negative 23 times six is 18 in 18 minus two. Gives us 16 and 16. Does people 16. So you know that B equals two.

Tomokazu Switzer · Answer

problems. 39 arrests, solving equations and then check our solution. All right, so we want to isolate our absolute value. First toe isolator. Absolutely. We&#x27;re gonna divide by three. So we hired this entire equation by three, reviving both sides by three. So that&#x27;s gonna give us absolute value to a plus seven equals. Now we divide each term by 33 A over three becomes just a and 12 over three becomes four. So make sure you divide each one each term. Right now, we&#x27;re going to do the rewrite. Rewrite is to a plus seven equals a close four, and then we&#x27;re gonna write the negative version. So it&#x27;s to a plus seven. It was the opposite of a plus four, but then we saw them separately. We have available on both sides. We don&#x27;t want that. We&#x27;re going to give it the terrible from one of the sides. I prefer to give him from the right hand side when convenient. So here, to a minus eight, that&#x27;s like one a. So to a minus one a is just a one day or just a and the A&#x27;s gone on the right hand side. And I was struck several from both sides, and we get a horse negative three over here. We want to distribute that negative on the right hand side that because negative a minus four now we add a to both sides. Give it from the right. So it&#x27;s two a plus one a, which is three a and struck seven from both sides. And with your three A equals negative 11 divided by three and we have a was negative 11 3rd All right, let&#x27;s check our solutions. I have a feeling we&#x27;ll run out of space. So sorry if I write to small home, so go back to the original. So it&#x27;s three times the absolute value off. Two times today. We want to check a willing to check. First is negative. Three. So plugging *** three for a plus seven is that equal to three times negative? Three plus 12. Remember, whenever we&#x27;re checking a problem, we gotta put our value into all instances of that rare. So we had a on the left and right. So we place both of them with the same number of neck and three. All right? And that&#x27;s a question mark. Are those highs equal So it&#x27;s retires later. Three&#x27;s negative. Six and three times Negative. Negative. Nine. Continuing negative. Six plus seven is one near nine. Plus 12 is three. Absolutely. I won this one and three times. One is three. So yeah, three street that worked. Let&#x27;s check the other one. Eyes going to times negative. 11 3rd Oh, joy. So negative. 11 3rd plus seven. Is that equal to three times negative? 11 3rd plus 12. Well, all right. Two times negative. 11 3rd nothing reduces their. So remember tools, like having two over once and you multiply straight across. So two times Negative Elevens. Negative. 22. One times three is three. I had the seven. Is that equal to on the right hand side of The three is reduced. So, what have these mean, negative? 11 plus 12. Okay. All right. And then continue on the left hand side. Negative. 22 3rd Ah, seven is the same as 21 3rd Okay, So you want a common denominator of three to put a three under the seven, you have to multiply the seven by 21 right? Gonna keep it the same. Number seven and 21 3rd are the same thing, right? I just rewritten. Seven is 2130. Uh, this is probably step. You&#x27;re not required to show where changed like that. Negative 11 plus 12 is one, and but I can now do the math. Negative. 22 3rd plus 21 3rd is negative. 1/3 around space here. Negative 22 plus 21 is negative one, and the denominator stays the same. So that&#x27;s how I got negative. 1/3. I want to continue over here where there&#x27;s more space. So I&#x27;m just copying what I have down there. All right, so absolute value of negative 1/3 is positive. 1/3. That&#x27;s right. Absolutely. And three times 1/3 three&#x27;s reduced you want. So that works. So one equals one. So both of them work both of these work Date was never three work. It was naked. 11 3 Negatives. Boo was negative. 11 3rd work. So my solution set is negative. Three and negative. 11 3rd That&#x27;s our answer

Lauren Shelton · Answer

All right, so in this equation, my goal is to get the variable a completely by itself. So since I have an equation, both sides of the equation of to be bounce at all times, I&#x27;m gonna draw a lot in that shows I&#x27;m bouncing both equations. I want to get the variable a completely by itself in an adding aid to seven. So I want to move this seven to the other side of the equation. So my question is, what&#x27;s the opposite operations of addition? Well, it&#x27;s just subtraction. So instead of adding seven, I&#x27;m going to subtract seven in order to get rid of it from the left side. But whatever I do, the one side, I also have to do to the other side. So I&#x27;m gonna track seven from the right set this well on the left side. I could just bring down my variable. A seven minus seven is just zero. Right. Those cancel out so I don&#x27;t have to write plus zero over here in this right, a equals negative. Three minus seven. Great. Let&#x27;s say I am in debt $3 then I pay for something. That&#x27;s $7. I&#x27;m still in debt, but im in debt even more so. Negative three, minus seven or negative. Three plus innings. Seven. His name 10. And then, since I have a completely by itself on the left side of the equation, I&#x27;ve finished this problem.

Amanda Stone · Answer

in this problem were given the equation three X plus one equals seven and were asked to solve this equation and to check our solution. So the first thing I want to do is get all of my numbers toe one side and all of my variable terms to the other. So I&#x27;m going to begin by subtracting one from both sides of the equation because this will get rid of that one on the left side. And that leaves me with three acts on the left and seven minus one is six. So Lisa was six on the right from here to get that X all by itself, I&#x27;m going to divide both sides by three. This will cancel out that three on the left solve X equals six divided by three, which is to so to check this, you can either start with your original equation or you can use the version that&#x27;s a bit more consolidated, that we&#x27;ve compressed a bit more and put our terms on either side together. So I&#x27;m going to go ahead and use the 2nd 1 three x equals six. If we pulled in to to this, we get three times two equals six, which gives us six equals six

Joshua Utley · Answer

okay. To solve this absolute value equation, we first need to isolate the absolute value. And we can do that by subtracting seven on both sides. So 22 minus seven is 15. So I have minus five day and the absolute values is equal to 15. And now I need to split that into two separate equations. So I have minus five is equal to 15 minus five is equal to minus 15 as well. So when I solve here to divide by minus five, I&#x27;m going to get a Z equals minus three and same thing here, denied by minus five. And here again, a is equal. Positive three. Now we have to check. So if I check here with my minus three minus five times minus three in the absolute value is 15 15 plus seven is 22. So this works. And then for a equals three, it&#x27;s also going to work. It&#x27;s minus five times three is minus 15. Absolute value of it makes it 15 15 plus seven is 22. So both of these solutions work. And here&#x27;s your sort of solutions

Problem

Solve for the variable and check. Each solution i…

Problem 25 Hard Difficulty

Solve for the variable and check. Each solution is an integer.
$(3 a+7)-(a-1)=14$

Answer

$a=3$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Anna Marie V.

Caleb E.

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Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

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$a=3$

Algebra 2 and Trigonometry

Anna Marie V.

Caleb E.

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Absolute Value - Example 1

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Ann Xavier GantertAlgebra 2 and Trigonometry

Anna Marie V.

Caleb E.

Kristen K.

Michael J.

Ann Xavier Gantert

Algebra 2 and Trigonometry