Question

What is the value of x in the triangle to the right?

Answer 1

The sum of all angles in a triangle is 180. What equation can you therefore write?

Answer 2

Here's a good image that can help you.

Answer 3

So that's two angles you're adding up. What's the third angle's value?

Answer 4

The third angle value is 7x + 3

Answer 5

So if we were to add up all those angle values, what do we know for sure it would be equal to?

Answer 6

Where did you get 138 from?

Answer 7

So that would represent all the angles of the value being added up. Now, refer to what I said at the beginning of this post. What number is universally known as the sum of all angles of a triangle.

Answer 8

Yes, therefore what equation could you write, knowing these two pieces of information.

You have the sum of all angles of this triangle, and you have the sum of all angles of any given triangle.

Answer 9

If the sum of all angles of a triangle is 180, doing 138 + 180 would create a shape much different than a triangle.

Here we are trying to write a true equation, basically something that is a true statement about this situation. This will help us solve for x as we will be able to use algebra.

So in this case, we could write:

\[7x + 3 + 50 + 83 = 180\]
Simplify the left side
\[7x + 138 = 180\]
Then continuing we can solve for x

This above statement is true because the sum of all angles of this given triangle would equal the sum of all angles of any given triangle.

Answer 10

Does that make sense?

Answer 11

Okay, good. Do you know how to solve for x here?

Answer 12

Well, the goal is to leave x alone on one side of the equals sign, so we can get something that looks like: x = ____

This is what's known as 'isolating x'

Answer 13

The first step to isolating x here would be to subtract 138 from both sides of the equation.

Answer 14

Remember to subtract it from both sides

Cause if you subtract 138 from 138, aka, 138 - 138, you get 0. This helps to isolate x or leave it alone.

Answer 15

No, it would look like this

Answer 16

Since 7x + 138 = 180 is a true statement, we have to keep it true. So whatever you do to one side of the equal sign, you must do to the other.

Answer 17

First figure out what 180 - 138 is

Answer 18

Correct. So now we have

7x = 42

Now you asked what we're supposed to do with 7x. Keep in mind that when we had 1x + 138, we subtracted. That's because subtraction is the opposite operation of addition. Since 138 was being 'added' onto 7x, we needed to subtract from it.

Now here we have 7x. This can be rewritten as 7 times x. What therefore do you think we should do to 7x?

Answer 19

If you multiplied 7x by 42, you would get 294x. Then whatever you do to one side, you would have to do to the other side, so you would do 42 times 42 and get 1764.

You would end up with 294x = 1764.

Keep in mind that what you want to do is isolate x. In this case, you want to be removing numbers / making them smaller.

Answer 20

Lets go back to 7x = 42. What do you think we should do? Keep in mind what I said about opposite operations. We had addition with +138, so we did subtraction. What's the opposite operation of multiplication?

Answer 21

Correct. As you may know, whenever you divide a number by itself, what do you get?

Answer 22

Yes. Therefore what should we do to both sides of the equation?

Looking at: 7x = 42

Answer 23

How do we get x alone?

Answer 24

Multiply by 1?

Answer 25

If we multiply it by 1, we just get the same equation 7x = 42

If 7x is basically 7 times x, what can we do that would be the opposite of it, and turn it into x times 1?

Answer 26

I'm stumped- I don't know. would we divide 7x times x

Answer 27

Almost. We want to divide both sides by 7.

If we do 7x / 7, we get x, now it's completely alone.

Answer 28

All you have to do is do 42/7

Answer 29

42 divided by 7 is 6

Answer 30

Correct, so now you have the value of x (:

Answer 31

Ohh this makes so much more sense. Thank you for walking through that with me

Answer 32

No problem. I saw that you've been doing a lot of geometry + algebra so I wanted to give you a walkthrough, I think it'll help you a lot.

Answer 33

You can always bookmark this post and come back to it if you forget what steps to do.

Answer 34

Okay I'll go ahead and do that. I really appreciate this :)

Answer 35

No problem.

For most of geometry questions like this, it's just:
1. Creating a true equation
2. Solving for x by isolating it.

Good luck in your math endeavors (: