Solve the given linear equation. Check your solution. − 5 − y = 3 ( y + 9 ) -5-y=3\left(y+9\right)

Here we're asked to solve the given linear equation and then check our solution. The equation that we're given here is negative five minuteus y equals three times y plus nine. So let's get started with our steps here. The first thing we want to do is simplify both sides of our equation, which we can do by distributing anything into parenthesis and combining like terms. Here I can see this three that needs to get distributed to y and nine, so let's start there. I'm going to keep this left side of my equation the same because nothing needs to get simplified and just focus on this distribution of my three. So three times y will give me three y and then three times nine will give me 27. So I have positive 27 there. So everything is fully simplified on either side of my equation now. And I can move on to step two. Using my addition and subtraction properties of equality to collect all variable terms on one side and all constant terms on the other. Remember, it doesn't matter which side we put variables versus constants on so long as they're opposite sides and we put all those variables together, all the constants together. So we have this variable term at negative y and we have this three y. So I'm going to start with my variable terms. I want to move this negative y over to the other side, which I can do by adding y. If I add y on one side, I have to add it on the other. That's what my addition property of equality tells me. So I end up with just negative five because negative y and positive y canceled. And then I have three y plus y, which gives me four y. So I have four y plus 27 over here. Now, since I have my variable terms all together, I want to move this 27, my constant, to the other side of my equation, which I can do using subtraction. So subtracting 27 on both sides, that will cancel that positive 27 out. And I have negative five minus 27, which gives me negative 32. So I have negative 32 equals four y. Now from here, I can move on to step three using my multiplication and division properties of equality in order to fully isolate my variable. So I have this four y here. Four is multiplying y. So I can get rid of that multiplication by the four by dividing by four because that's that opposite operation. Whatever I do to ones that I have to do to the other, so making sure I divide that negative 32 by four as well. So these fours will cancel out. I have negative 32 divided by four, which gives me negative eight. So I have negative eight equals my variable here y. And this is my solution. Now I, of course, want to check my solution to make sure that I did this correctly by plugging that negative eight back in for y to my original equation. I have two instances of y here, so I want to make sure that I replace both of them with that negative eight when checking. So I have negative five minus negative eight equals three times negative eight plus nine. So we're checking, is this a true statement? So I have negative five minus negative eight. We know that two negatives make a positive, so I have negative five plus eight, which is positive three. And then I have three equals three times negative eight plus nine. Negative eight plus nine, just focusing inside of those parentheses, is going to be positive one. So this is three times one. Is this a true statement? Well, that three stays the same. And then three times one is just three. So I end up with this statement that three equals three. Definitely a true statement as those are the exact same value. So that tells me that I did solve this linear equation correctly. My solution is that negative eight equals y. Let us know if you have any questions and let's keep practicing.

2. Linear Equations and Inequalities

Solving Linear Equations

Beginning & Intermediate Algebra

2. Linear Equations and Inequalities

Solving Linear Equations

Struggling with Beginning & Intermediate Algebra?

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Multiple Choice

Solve the given linear equation. Check your solution.
$- 5 - y = 3 (y + 9)$

$y=-8$

$y=8$

$y=-3$

$y=3$

Verified step by step guidance

Start with the given equation: $-5 - y = 3\left(y + 9\right)$.

Distribute the 3 on the right side to both terms inside the parentheses: \$3 \times y$ and $3 \times 9$, giving $-5 - y = 3y + 27$.

Next, get all the terms involving $y$ on one side and the constants on the other side. You can do this by adding $y$ to both sides and subtracting 27 from both sides: $-5 - y + y - 27 = 3y + y + 27 - 27$ which simplifies to $-5 - 27 = 4y$.

Combine the constants on the left side: $-5 - 27$ becomes $-32$, so the equation is now $-32 = 4y$.

Finally, solve for $y$ by dividing both sides of the equation by 4: $y = \frac{-32}{4}$.

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Struggling with Beginning & Intermediate Algebra?

Solve the given linear equation. Check your solution.−5−y=3(y+9)-5-y=3\left(y+9\right)

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Solve the given linear equation. Check your solution.
$- 5 - y = 3 (y + 9)$