Determine whether each equation is an identity, a conditional ...

Question

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. (1/2)(6x+20) = x+4 +2(x+3)

Accepted Answer

Welcome back. I am so glad you're here. We are given this linear equation where we have 3/4 times 12 X minus 32 on the left hand side. And that's equal to seven X plus two plus two times parentheses X minus 13. On the right hand side. We need to find the solution and then choose the type of linear equation. So let's start off by distributing where we have something squished up against the parentheses here. On the left we have this 3/4 that needs to be distributed to the 12 X. Into the negative 32. And on the right hand side we have this too. That needs to be distributed to the X and to the negative 13. So let's do that distribution 3/4 times 12 X. Well taking 3/4 times 12 X. The 12. And the four are going to reduce. So that's three times three X. Which will be nine X. And then 3/4 times negative. 32. Again the 32 the four will reduce. So that's three times negative eight which is negative 24. Now, that will be equal to on the right hand side for that seven X plus two. We can drop the parentheses. There's nothing that needs to be distributed there. And those aren't like terms. So we can't combine them. Now let's distribute that two to the X -13. So two times X. Is plus two X. And two times negative 13 is negative 26. All right now let's combine like terms on the right hand side, we have this seven X. And this two X. That can be combined. That would combine to nine X. And then we also have this plus two minus 26 that can be combined. And two minus 26 is going to be a minus 24. Bringing that down and bringing down the left hand side nine x minus 24. Look at this, our left hand side is exactly equal to the right hand side. We could keep going we could subtract nine X from both sides of the equation and then we'd have no exes and then we could add 24 to both sides of the equation. And then we'd have no 24 as we have no regular numbers at all. This would be zero equals zero. And we recall from previous lessons that this is a special condition. This is an identity equation where one side equals the other side. And this solution set is all real numbers. So we can put a set and we can say all real numbers for our solution set. Now we look at our answer choices and this matches with answer choice. A Well done. We'll catch you on the next one

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. (1/2)(6x+20) = x+4 +2(x+3)

Key Concepts

Types of Equations: Identity, Conditional, and Contradiction

Solving Linear Equations

Distributive Property

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