Question

Help! My Algebra 1 teacher handed out a hand written assignment. I need some help on how to solve this equation: 5x – 5 >= 10 or -3x + 1 >= 13 She says I have to show all of my work. I'm not that good on solving these equations. It would help me in the second part of the assignment also. I need to graph the inequality in the second part

*if you notice answers below, don't mind them. Their from a different question. I'm unsure of how to delete previous questions and ask new ones other then editing them and asking a new one*

Can someone please help me? This is due by midnight

Answer 1

I'll help you with the first one

but you post each question per post oki?

Answer 2

oki!

Answer 3

A. x<= -10
First one^

Answer 4

Multiply each sides by \(2\), than simpltiply \(5\) by \(2\) to \(10\)
\[\ 10≤−x\]
And multiply each side by negative one
\[\ −10≥x\]

Than switch those side, \(x≤−10\) or as \(x<= -10\)

Answer 5

*Simplify >_>

Answer 6

Here. This file has both the equation and the graph. If your able to help, please do.

Answer 7

The first half has already been helped with, unless you still don't understand it.
The second half of the same question was over looked: \[-3x+1\ge13\]
Would you like help with that?

Answer 8

Yes please

Answer 9

You must isolate x first. I'll do the first step.
\[-3x+1\ge13\]
\[-3x \ge 12\]
Could you try to do the rest?

Answer 10

I could try. But I'm not really sure what else to do in order to try

Answer 11

You want x as one unit. You want x as x (it looks the same as 1x), not -3x.

Answer 12

Would I want to divide both sides by -3 (if I have to divide) or one side by -3 and the other by positive 3?

Answer 13

Both sides by -3. You will also flip the sign because the sign flips when either multiplying or dividing

Answer 14

Being that -3 cancels itself out and i get -4 when i divide -3 by 12, how would I set up the inequality?

Answer 15

Applying the rules (sign changing, x isolated...) it would look like \[x \le-4\]
Did you understand when the others helped you with the 5x-5>= 10?

Answer 16

Not really no. This concept is a bit confusing for me

Answer 17

Ok this one looks easier. Add five to isolate x
\[5x-5\ge10\] changes into
\[5x \ge15\]

Answer 18

Make sense?

Answer 19

Yep

Answer 20

The last step in turning 5x into x is to...?

Answer 21

Cancel out 5? I'm honestly not really sure

Answer 22

Divide all sides by 5. The end result would be...?

Answer 23

X ≥ 3?

Answer 24

Yes!

Answer 25

The second half is visually putting the two inequalities together

Answer 26

How exactly would I do that?

Answer 27

By taking each inequality and graphing it on a number line. Let's take a finished one.
\[x \ge5\]
and plotting it on the line. The line should look like this:

Answer 28

The picture looks bad, but each tick represents a number with each side extending to infinity

Answer 29

\[x \ge5\] would start on exactly 5 and stretch infinity positively. The line underneath the > means equal, so the symbol entirely would 'exactly 'x' (whatever number that might be) and above.' Is 6 bigger than 5? Yes, so we say \[6\ge5\] Understand?

Answer 30

Yep

Answer 31

Then the other one would extend in the opposite direction correct?

Answer 32

Yes. \[x \le-4\] would strech the other way.
You'll be seeing 'and' and 'or' a lot of times. Here are the rules.
And: the x is in between the two inequalities
Or: the x is either in one inequality or the other but not both.

Answer 33

In this case, it's an 'or' so the unknown x is in one inequality. This will show a gap
REMEMBER: In inequalities there is no definite number for x hence the IN in inequality.

How would the number line look like with the inequalities shown?

Answer 34

I don't think that the inequalities would be connected on the graph. So one would be infinitely positive and the other infinitely negative

Answer 35

If the X was in between both or 'and', then they'd be connected. Being that 'or is in there, then they'd go in the opposite direction of each other

Answer 36

My hint with remembering with the direction inequalities is simple: the arrow points the direction it's headed. This applies to all inequality signs.
\[> meaning \rightarrow on number line\]
\[< meaning \leftarrow on number line\]