Question

Find the solution to the following inequality:
x - 10 < 3

A. x < -7
B. x\leq -7
C. x\leq 13
D. x< 13

Answer 1

B \[x\leq -7\]

Answer 2

\[ C. x\leq 13\]

Answer 3

What do you think the first step is in solving this inequality?

Answer 4

I know all the steps but I don't understand the underline under the < sign

Answer 5

Ahh ok. That just means it is less than or equal to. For instance, if you had x<4, it would be all values less than 4 but not 4 itself. However, if you had:
\[x \le 4\]
It would be all numbers less than 4 as well as 4 itself.

Answer 6

I don't quite follow. So Every number is less than 4 ?

Answer 7

Let's start with x<4. Do you understand what this is stating? This means that the value of x is everything less than 4, but nothing equal to 4 or greater than 4. Does that make sense?

Answer 8

Yes X < 4 basically means X is not equal and is less than 4. Stating every number before 4 is less than 4

Answer 9

but the underline < doesn't make any sense to me

Answer 10

Right. So now, the underlined < sign just means you're also going to say that x=4 is true. So x<4 AND x=4. This means that everything less than 4 and 4 itself is the value of x. Does that help you understand?

Answer 11

So that means X also = 4. but X is also less than 4?

Answer 12

Exactly. So x is all of the values less than 4 and x is the value 4 itself. They made it into a new symbol which combines the equals sign and the less than sign so they don't have to say x<4, x=4 every time.

Answer 13

-10 + 10 = 0.

7 + 10 = 17.

Answer 14

I forgot actually what am I supposed to do now?

Answer 15

Which problem is that from?

Answer 16

The question I posted. Lol

Answer 17

Ahh. Where did the 7 come from? I see:
x-10 < 3

Answer 18

oh fail XD. I thought of 7 and wrote it...

Answer 19

I was looking at A,B, C and D

Answer 20

so basically 3 + 10 = 13

-10 + 10 = 0

Answer 21

Right, so what inequality do you end up with?

Answer 22

See, i don't know if it's C or D

Answer 23

Ahh. So you can never switch from a regular < or > to a \[\le or \ge\] during a problem like this. If you are finding the solution to the inequality, it will either keep the bar, or never have it throughout the problem.

Answer 24

ohh

Answer 25

So D

Answer 26

Right.

Answer 27

Hello @mathmale

Answer 28

A quick review:

Find the solution to the following inequality:
x - 10 < 3

Add 10 to both sides. Result: x<13. That's all. Finished.

Supposing that you had

\[x -3 \le 10\] to solve:

Add 3 to both sides.

Result: \[x \le13\] END!

Answer 29

Hello, Zeronknight!

Answer 30

oh! Thank you for the explanation. I actually think I have a better understanding now.
(I don't know if people would take this as sarcastic or not, but it's not sarcastic)

Answer 31

My pleasure. Absolutely no suspicion of sarcasm!
Just wanted you to know that the basic solution is quick and straightforward.

Answer 32

Just one question? When would I use the underlined <?

Answer 33

Well it would have it from the start right? But how would it exactly play in a problem?

Answer 34

When it is equal to

Answer 35

Oh. So when X is equal to the number? I understands what it means, but not how it would right in a problem.

Answer 36

< means "less than."
\[\le .\] means "less than or equal to."

Answer 37

You will encounter both in typical "inequality" problems.

Your task is mainly to understand the difference between the two symbols and how to solve inequalities that involve them.

Answer 38

Oh

Answer 39

That makes much more sense, thank you.

Answer 40

My great pleasure. Merry Christmas to you!

Answer 41

Merry Christmas too you too! Surprised anyone has said that. I usually encounter Happy Holidays XD

Answer 42

;)

Answer 43

XD

Answer 44

People try too hard to be politically correct. Every so often I'm politically incorrect. ;)

Answer 45

XD Well then. owo