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Question

Solvre Ihe equalion Then delermne whether Ihe equation Sx + [email protected]; cond ional equation, Or an inconsistert equatioWhat Is the solution? Select Ihe correct choice belw and, necessary; fill in the answer box to complete your choiceThe equation has single solutlon_ The solution set Is The solubion set is {x | x Is number} solution set isWhat typc Gqualion Ihts ?inconsistent equaticn conditional equalion identit;C -Jns er

Solvre Ihe equalion Then delermne whether Ihe equation Sx + 2x+6 @dendity; cond ional equation, Or an inconsistert equatio What Is the solution? Select Ihe correct choice belw and, necessary; fill in the answer box to complete your choice The equation has single solutlon_ The solution set Is The solubion set is {x | x Is number} solution set is What typc Gqualion Ihts ? inconsistent equaticn conditional equalion identit; C - Jns er



Answers

Find each solution set. Then classify each equation as either a conditional equation, an identity, or a contradiction. $$ 3 x-(8-x)=6 x-2(x+4) $$

Or being asked to determine if the given equation is an identity, a conditional equation or contradiction. And the only way to determine that is to actually solve the equation. So let's go ahead and do that. Well, first thing I can do is remove my parentheses by distributing well. 0.3 times X is just 0.3 x and 0.3 times two is positive. 20.6. Then I'll distribute the negative 0.5. Well, negative 0.5 times X is negative. 0.5 x and negative 0.5 times two is negative one. And then I'll leave the right hand side as it Now. I see we have, like, terms on the left hand side. Souls combined. Notes. We have 0.3 x minus 0.5 x. Well, that's negative. 0.2 X and then we have 0.6 minus one, which is negative 10.4 and again, we'll bring down the right hand side. We'll take a look. Both the left hand and the right hand side of the equation are the exact same thing. They're both negative 0.2 x minus 0.4. So what that means is our original equation is an identity, meaning that they're the exact same thing. And the solution set for any identity is all real numbers. So that will be our solution set.

Problem or first being asked to determine if the given equation is an identity, a conditional equation or contradiction. Well, the only way to determine that is to solve. So let's go ahead and do that. So first, we're gonna need to remove the parentheses by distributing. So on the left hand side, we distribute the one half well, one. Halftime. Six x is three X and then we have one half times 20 which is positive test Now. On the right hand side, we have X Plus four, and now we'll have to distribute the two well. Two times X is two X and two times three is six. Now. I see we have, like, terms on the right hand side, so let's combine those. So we're gonna have three X plus 10 on the left. On the right hand side, we have X plus two X. Well, that's three X and then we have four plus six, which is 10. We'll take a look at what we have. Both the left hand side and the right hand side are both the exact same. They're both three X plus 10, which means that our original equation is an identity because it's the same on both sides. I remember the solution set for an identity is all real numbers because no matter what value substitute, then it will make the equation true. So our answer is that it's all real numbers.

For this problem. We want to determine what type of equation our linear equation is, whether it's an identity conditional or a contraction. And we start with 1/2 six x plus 20 equals X plus four plus two X plus three. And we first want to distribute out all of our constant. So we have three x plus Tim because X plus four plus two X plus six. Now we can add like terms to get three X plus 10 equals three X plus 10. And now if we subtract three X plus 10 from both sides, we would get zero equals zero, which means that the solution is an identity because we have zero equals zero and the solution is all riel numbers.

Elects simplified board saves and then will decide whether this is contradicts our identity. Our condition equations so first play distribution over here so Putin's record nine minus minus into minus plus on 3 to 6 x and again minus minus plus a +34 record close. People tell X Plus 42 No, this is six x plus nine plus 12 which is 21 people. Tell X Plus four people. And then he was this stability law. You'll find this tell X Plus 42 equal to tell X plus 42 using distributed. So this is proof of all the value of X if you order. This is true for all the value of X Supposed I had minus 14 to both sides. Surgical to tell, Executed telex. This is true for all that I know of. X are supposed add minus X herbal side physical 42 it will 42. So either this artist, So both are true so that ever equation It's true for all the value of X, all the will of X, that poor it isn't identity. Therefore therefore it is identity


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