The equations in Exercises 79–90 combine the types of equations w...

Question

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation.

2/x + 1/2 = 3/4

Accepted Answer

So this problem tells us to determine whether the equation is an identity conditional equation or inconsistent equation after solving the equation. So let's go ahead and try and solve our equation. So if you look here you have nine over a plus two thirds equals 7/6. So I want to solve for a the first thing we can do is actually get rid of this two thirds. So I'm going to move the two thirds over to the other side. So so we have -2/3 -2/3. So over here we're gonna have 76 -2/ 7, -2. That's however they don't have the same denominator so we can't subtract them directly but we can however rewrite our two thirds equation to have the same denominator. So 2/3. What kind of think of 2/3? We want to get it to something over six. Well how do we get from 3 to 6? We multiply by two. So at the top we can multiply by two ticket. Four, meaning two thirds is equal to 4/6. So going further we have 7/6 minus 4/6. That's equal to 3/6 which also simplifies to one half. Now if we go back to our original equation, I'll rewrite this, we have nine over a Equals now 1/2. So we still want to solve for a which means we're gonna multiply both sides now by a. This is gonna move our A. To the other side. Now we have our is canceling out here. nine left over equals 1/2 a. Finally we want to get rid of that one half in front of the eight something that divide everything by one half. So we're left with a equals now. 9/1 half is the same thing as saying The same thing as saying nine times 2 because we have a fraction on the bottom, we would take the reciprocal and multiply or flip and multiply. So we have nine times two, which turns out to be 18. You can always put that in the calculator to determine that as well if you're unsure. So you notice here we have one solution. Our solution is 18. So since we have one single solution, our answer is A. Which is a conditional equation where we have one solution. Okay, I hope to help you solve the problem. Thank you for watching. Goodbye.

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