solve-for-the-variable-and-check-each-solution-is-an-integer-2b-33b4b14

Question

Solve for the variable and check. Each solution is an integer.
$2(b-3)+3(b+4)=b+14$

M S · Accepted 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.

Aditya Sood · 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.

Angela Guo · Answer

to solve the secret Asian that&#x27;s multiply both sides by the L C. The LCD in this case is 12. So the left side would have creepy plus six and then the right side. That would be four b minus. So we&#x27;re gonna subtract three, be on both sides, and then add three on both sides. So we end up with nine is equal to. So now we just have to check, um, our answer by putting it back into the original creation. So that and sipping 9/4 plus 1/2. And is that equal to nine over this three minus 1/4. Okay, so what&#x27;s your left side? First? 9/4 plus one over to. That&#x27;s the same as tool before. And then the right side, um, 9/3. That is just three. So, three, you can change that to 12 Well, before minus 1/4. So this is the left side is going to be 11/4, and in the right side, that&#x27;s 12 minus one, but also 11/4. So we&#x27;re good

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.

Ashley Volpe · Answer

So we have the equation three times a minus three equal to two times a plus. For if we distribute on the left, we get three a Moniz, not could we distribute on the right. We get to a plus eight. I&#x27;m gonna move my to A to the left. Since the A&#x27;s are going to the looked, I&#x27;m gonna move the non to the right so that I get a equal to 17 to check it. We&#x27;re gonna plug 17 in. So we have three times 17 minus three equal to two, two terms. 17 plus four 17 monastary is 14 17 plus four is 21 three times 14 is 42 and two times 21 is 40. So that checks and my answer is a equal to 17.

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

Problem

Solve for the variable and check. Each solution i…

Problem 26 Medium Difficulty

Solve for the variable and check. Each solution is an integer.
$2(b-3)+3(b+4)=b+14$

Answer

$b=2$

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Absolute Value - Example 1

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$b=2$

Algebra 2 and Trigonometry

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Absolute Value - Example 1

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Ann Xavier GantertAlgebra 2 and Trigonometry

Alayna H.

Caleb E.

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Michael J.

Ann Xavier Gantert

Algebra 2 and Trigonometry