Question

What is the solution set of (3x - 1)2 = 5?

Answer 1

Hello, Lashay, I hope you're enjoying your stay so far at OpenStudy.

The first step to solving an equation is using the PEMDAS sequence. \[(3x - 1)2 = 5\]
You can see there are no parenthesis that can be added,
You can see there are no exponents are division.
However, there is multiplication that can be performed.

You want to use the distribution property to distribute the 2.
The distribution property states: \[(z + y)x = xz + xy\]

Lets apply that. Your first step is as shown: \[(3x - 1)2 = 5 \rightarrow 6x - 2 = 5\]
This is upon distributing the 2 throughout the terms located inside the parentheses.

So, the next step is getting rid of the -2 by perform the opposite action.
Can you simply it from here? Go ahead and give it a try!

Answer 2

how do you set up the problem I still don't get it

Answer 3

No problem.

Are you aware of what the distribution property is?

Answer 4

yes

Answer 5

Alright. Then you understand that the distribution property makes expressions equal.

For example: (1 + x)z. Multiplying both 1 and x by z will maintain equality. In equations must be equal.

So, given (3x - 1)2 = 5, you first need to simply the equation before solving it, correct?

If I had: 2 + 2 = 4. I'd first need to simply the 2 + 2, and say 4 = 4, which is correct, right?

The same rule applies. If there are operations that can be perofmred I must perform them before solving teh equation.

Going back to the original equation: (3x - 1)2 = 5
I see the an operation of distribution can be peformed, so I must perform it.

I now have: 6x - 2 = 5. Because I did 2 * 3x and 2 * -1.

With: 6x - 2 = 5, I then have to add 2 to 5, which gives me 6x - 2 + 2 = 5 + 2
Which comes out as: 6x = 7. Now, I see 6 is being multiplied by x, so I need to divide 6 by 7.

Now, I bet you're saying, "woaahh, slow down there. This is too much for me to take in."

Well, it is hard learning it for the first time. So please watch the short 2minute video below to grasp an understanding of why we perform the opposite action to both sides of teh equation.


https://www.khanacademy.org/math/algebra/introduction-to-algebra/algebra_why/v/why-we-do-the-same--thing-to-both-sides--simple-equations

Answer 6

thank you so much :)

Answer 7

No problem. Come back to OpenStudy and tag me if you need help!

Answer 8

Ok i sure will