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. -6(2x+1) - 3(x-4) = -15x+1

Accepted Answer

Hey everyone here we are asked to find the solution and choose the type of linear equation for the given equation. Where we have 21 times the quantity of one minus x plus 20 times the quantity of x minus three is equal to 39 minus X. Now to find the solution of this equation, we just need to solve for X. So we want to begin by factoring in this 21 factoring in the 20 on the left hand side of our equation. So doing this, our equation becomes 21 minus X plus 20 X minus 60 is equal to 39 minus x. So now we just need to combine our like terms on the left hand side of our equation. So we have 21 minus 60 which is just negative 39 then we have minus X plus 20 X which gives us minus X. And this is equal to 39 minus x. So now we can just get our negative X to alone on the left hand side of our equation by just moving over this negative 39 to the right hand side. So to do this we need to add 39 to both sides of the equation and then we have negative X. Is equal to 39 plus 39 minus X. And now combining our like terms, we have that negative X is equal to 78 minus X. And now we need to get all of our X terms on the same side of the equation. So we can move the X term on the right hand side to the left hand side. And we do this by adding X to both sides. So we have negative X. Plus X is equal to 78. And now simplifying, We end up with just zero is equal to 78. Well looking at our solution here, we have zero is equal to 78. Well this is a false statement. We know that these two values are not equal to each to each other. So we have a contradiction, a contradiction equation. And that tells us that our solution set is an empty set here. So we denote that as a this circle with a slash through it. And with this we are left with answer choice C. Where we have an empty set and a contradiction equation. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. -6(2x+1) - 3(x-4) = -15x+1

Key Concepts

Types of Equations: Identity, Conditional, and Contradiction

Solving Linear Equations

Distributive Property

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