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### Course: Digital SAT Math>Unit 8

Lesson 9: Radical, rational, and absolute value equations: medium

# Radical and rational equations — Basic example

Watch Sal work through a basic Radical and rational equations problem.

## Want to join the conversation?

• Why is it called RATIONAL equations instead of just, say, equations?
• It's a description helping to classify what kind of equation it is. The term "rational equation" indicates that there is a denominator in the equation.
• I'm confused, if we're multiplying both sides by 4k-3, why does the 11 remain?
• If you multiply 3/2 by 2, what do you get? 3.

If you multiply 15/31 by 31, what do you get? 15.

If you multiply 11/(4k-3) by (4k-3), what do you get? 11.
• Don't you guys know the criss cross method?
• yh thats exactly waht sal did...
(1 vote)
• it took 5sec to solve. 🥷
• I'm still waiting for the other methods he talked about😂
• This was easy. (relatively)!
• why do we leave the answer in improper fraction instead of simplifying?
(1 vote)
• Since 17 is a prime number, the fraction can not be simplified. Also, in math, mixed numbers are not the preferred method of displaying fractions because mixed numbers sometimes look similar to improper fractions. 3 and 1/2 (which is 3.5) looks quite similar to 31/2 (which is 15.5).
• Isn't functions include radicals are NOT rational functions?
Here you talk about rational equations. So do you mean rational equations can contain radicals? I'm very confused. :(
(1 vote)
• two equations two unknowns
(1 vote)
• The rules of algebra, especially the addition property of equality, say that if we add 6 to both sides of the equation, we do not change the balance of the equation, and the two sides will remain equal.
So if we have 8k - 6 = 11
we can add 6 to both sides
8k - 6 + 6 = 11 + 6
∴ 8k - 6 + 6 = 11 + 6
8k + 0 = 17
8k = 17 now we use the division property of equality that says that we can divide both sides by the same amount (as long as that amount is not zero)
8/8 k = 17/8
k = 17/8
(1 vote)

## Video transcript

- [Instructor] What is the solution to the equation above? So we just need to solve for k. So one thing that we could do, well, there's a couple of ways that we could do it. One way is we can multiply both sides of this equation times four k minus three. So let's just do that. Four k minus three. It gets the four k minus three out of the denominator because four k minus three divided by four k minus three. As long as we assume four k minus three isn't equal to zero, that's just going to cancel out and be equal to one. And so this equation is going to simplify to four k minus three times two. And we can actually distribute this two. So this becomes two times four k is eight k. And then two times negative three is negative six. So eight k minus six is equal to, well, all we're left with is 11 over one, or we can just write 11. And so adding six to both sides, you could add six to both sides, and so those add up to zero. You're left with eight k is equal to 17. Now we can just divide both sides by eight, and we get k is equal to 17 over eight. K is equal to 17 over eight.