Solve the given linear equation. Check your solution. 2 ( x + 3 ) = 14 2\left(x+3\right)=14

this problem, we're asked to solve the given linear equation and then check our solution. The linear equation we're given here is two times x plus three equals 14. Now the very first thing we want to do here according to our steps is to simplify both sides of our equation by distributing anything that we need to into parentheses and combining any like terms. So let's do that here. I have this two that needs to get distributed to my x plus three. So distributing it to x gives me two times x, that's just two x, and then multiplying it by that three gives me six. So I have two x plus six equals 14. Now from here, we can move on to step two using our addition and subtraction properties of equality in order to collect all variable terms on one side and all constant terms on the other side. Now I only have one variable term, this two x, so I'm just gonna focus on my constants. Since my variable term is already over here on the left side of my equation, I'm gonna go ahead and move any constants over to the right. So I need to move that plus six over to the other side. Now in order to get that plus six to cancel over here, since it's being added, I can use subtraction. So subtracting six here using my subtraction property of equality to do this on both sides lets this cancel, leaving me with just two x. Then fourteen minuteus six will give me here eight. Then I have the equation two x equals eight and we're moving into step three, using our multiplication and division properties of equality to fully isolate our variable. Here, I just have this two multiplying by x. So in order to get rid of that multiplication to get that variable all by itself, I need to use division. So dividing by two on both sides leaves me with just x. And then I have eight divided by two, which will give me here four. So this gives me my solution here, x equals four. We have just one step left to follow here. That's checking our solution by plugging this back into our original equation. So putting four in for x to this equation, we get two times four plus three equals 14. We're checking, is this going to give us a true statement? So two times four plus three, four plus three will give me here seven. So I have two times seven. We're checking, is this equal to 14? Two times seven is 14, so I get the statement that 14 equals 14. This is definitely a true statement because these are the same exact value, so I know that I found my solution correctly, x equals four. Now there's actually another way that we could have gone about solving this linear equation. So I wanna walk you through that here as well because it may be useful to you as you continue on. Starting with our original equation, which was two times x plus three equals 14. According to our steps, we always want to start by simplifying both sides of our equation. And this will always work if we follow these steps in this order. But that's not to say that we could actually start with a slightly different step in solving this particular equation. Because we have only one instance of x and our ultimate goal here is to get that x all by itself, so we just wanna do whatever we can to get rid of anything else going on on that side of our equation, we could have actually started here by dividing out this two. So if I started here by dividing by two on both sides, whatever I do to one side I have to do to the other, those twos would cancel out, leaving me with just that x plus three. Then 14 divided by two would give me here seven. Then I could use my subtraction property of equality to subtract off three on both sides to get me that x equals seven minus three, which is four. Now this is the same exact answer that we got by following our steps. And again, these steps are a foolproof way to get a solution when working to solve a linear equation. But if you recognize early on that, hey, I could actually get rid of stuff slightly differently, Instead of following those steps exactly as written, I could go ahead and use my division property of equality because ultimately, we're just working to get our variable x all by itself. And dividing by two is one step that we could start with in order to do that. Now if you don't recognize that early on, that's totally okay. Remember, your steps will always work. And ultimately, no matter how you go about solving your linear equation, you should always always check your answer at the end by plugging it back into your original equation to ensure that you did it correctly. Feel free to let us know if you have any questions in the comments, and I'll see you in the next one.