Uploaded by videosbyjulieharland on 18.05.2011

Transcript:

>>Hi, this is Julie Harland

and I'm your math gal.

Please visit my website

at yourmathgal.com

where you could search for any

of my videos organized

by topic.

We're going

to translate sentences

into algebraic equations

or inequalities.

So we'll start with this one,

7 less than a number is 10.

Now what makes this a sentence

is it has this verb, is,

and usually that's what

separates an expression

from an equation.

So when you see the word is

that's kind of breaking

up where the equals sign

will be.

So we're going

to have the left side

of the equation,

which will be 7 less

than a number,

and the right side

which will be the number 10.

So is, that's

where the equal sign is.

Now we just look before the

word is and we've got what?

Seven less than a number

so that means we're

subtracting 7 from a number

so let's call the number n.

So N minus 7 will be 7 less

than a number on the left side

and then on the right side

both the equal sign

after the word is is just the

number 10.

And now we've just translated

7 less than a number is 10

into an equation.

Now if we were trying

to solve this,

usually you would define

your variables.

In other words you would say

I'm gonna let n be the number

that, in this video we're just

going to keep using n,

let that be the number.

So where it says a number

we're just gonna use the

letter n. You could use x, c,

a, any letter you want.

I like n for number.

Alright why don't you try this

one on your own

by putting the video on pause

and seeing

if you can figure it out.

Okay again we're gonna see

that we've got

that word is there,

5 more than a number is,

those are equal,

is twice a number.

That breaks up so left side

of the equation

with the right side

of the equation.

Alright so I've got the word

is, that's gonna be our equals

so we've got 5 more

than a number.

Okay, 5 more

than something means I'm

adding 5 to something

and I'm gonna add it

to the number and we decided

to use n for the number.

Alright now I've got the left

side of the equal sign

and then what

about on the right hand side?

We've got twice the number,

that means 2 times the number

or 2n.

Hopefully you got that.

Alright let's look

at this one, 4 is not equal

to the product of 2 and 3.

Hmm, a little tricky.

You see that word is again

but it's this whole part

that goes together,

4 is not equal so instead

of an equal sign we're gonna

use a not equal sign.

What's a not equal sign

look like?

Well, that's what an equal

sign looks like.

That's what a not equal sign

looks like.

You just put a slash

through it, not equal.

So now we've got the left side

of the equation is just the

number 4.

So we have 4 on the left side,

4 is not equal to

and on the right hand side we

have the product of 2 and 3.

Alright product

means multiplication.

So the product of 2

and 3 means we're gonna

multiply 2 times 3.

So we can just say 2 times 3

with a dot

or you could put a 2

parenthesis 3

to denote multiplication

and this makes sense.

Hopefully everybody,

4 is not equal to 6,

right cause 4

and 6 aren't the same number.

Notice there was no variable

in this one.

That's okay.

So this is still just taking a

statement and writing it using

the symbols.

In this case all the symbols

were just numbers

and the not equal sign.

Alright the sum of a number

in 8 is less than 14.

Again you see this word is

but you kind of have to look

at the context.

It says is less

than something.

So this time instead of is,

which would be equal,

we have is less than.

This symbol is written

like this, is less than.

So again we've broken

up what comes before

that is the sum of the number

in 8 and the sum, remember,

means addition.

So a number, we'll use n

and the other part of it is 8

so n plus 8 is less than,

right, what's

on the other side

of the equal sign, I'm sorry,

of the less than symbol, 14.

So now we've just translated

this sentence

into an inequality.

Both of these

on this page are called

inequalities

because they don't have just

an equal sign.

We've got a not equal sign

and we have a less

than symbol.

So these are called

inequalities as opposed

to equations

but they're still

algebraic inequalities.

I guess this first one is

actually just numerical,

there's no algebra.

So it's just an inequality

with numbers.

Alright here are a couple

for you to try on your own

and then we'll check them

so put the video on pause

and try these two.

Alright the first one,

4 decreased

by twice a number is 1 more

than the number.

Okay we've got just is this

time so that's gonna separate

the two parts.

So first we've got 4 decreased

by twice a number, hmm,

4 decreased by,

alright so I've got to start

with the number 4

and then I'm gonna decrease it

so I have to subtract

something from that.

What is it gonna be?

I'm subtracting twice a

number, that's 2 times n

so I write 2n.

And I've got is,

there's my equal.

Alright now we've got,

right hand side,

1 more than the number.

Alright 1 more

than something is I'm adding 1

to something.

What am I adding it to?

Whatever that number is,

same number,

n. So I've got 4 minus 2n

equals n plus 1.

So all we're doing

is translating.

We're not worrying

about what n is.

Alright and let's see this

last one, 3 times a number is

greater than or equal to 9,

hmm, tricky.

So I've got,

this whole part is greater

than or equal to,

that's this symbol,

greater than or equal to.

Alright so on the left hand

side of that I've got 3 times

the number,

on the right hand side I've

got 9.

So on the left hand side 3

times the number can be

written as 3n,

cause we're using n

to represent the number.

On the right side we've just

got the number 9

so now we've written 3n is

greater than or equal to 9.

So that's just a little

introduction

to translating some sentences

into equations

or inequalities.

Where there's an equal sign

it's an equation.

When you've got greater than

or a less than symbol or a not

to equal symbol,

then we're talking

about an inequality.

[ Silence ]

and I'm your math gal.

Please visit my website

at yourmathgal.com

where you could search for any

of my videos organized

by topic.

We're going

to translate sentences

into algebraic equations

or inequalities.

So we'll start with this one,

7 less than a number is 10.

Now what makes this a sentence

is it has this verb, is,

and usually that's what

separates an expression

from an equation.

So when you see the word is

that's kind of breaking

up where the equals sign

will be.

So we're going

to have the left side

of the equation,

which will be 7 less

than a number,

and the right side

which will be the number 10.

So is, that's

where the equal sign is.

Now we just look before the

word is and we've got what?

Seven less than a number

so that means we're

subtracting 7 from a number

so let's call the number n.

So N minus 7 will be 7 less

than a number on the left side

and then on the right side

both the equal sign

after the word is is just the

number 10.

And now we've just translated

7 less than a number is 10

into an equation.

Now if we were trying

to solve this,

usually you would define

your variables.

In other words you would say

I'm gonna let n be the number

that, in this video we're just

going to keep using n,

let that be the number.

So where it says a number

we're just gonna use the

letter n. You could use x, c,

a, any letter you want.

I like n for number.

Alright why don't you try this

one on your own

by putting the video on pause

and seeing

if you can figure it out.

Okay again we're gonna see

that we've got

that word is there,

5 more than a number is,

those are equal,

is twice a number.

That breaks up so left side

of the equation

with the right side

of the equation.

Alright so I've got the word

is, that's gonna be our equals

so we've got 5 more

than a number.

Okay, 5 more

than something means I'm

adding 5 to something

and I'm gonna add it

to the number and we decided

to use n for the number.

Alright now I've got the left

side of the equal sign

and then what

about on the right hand side?

We've got twice the number,

that means 2 times the number

or 2n.

Hopefully you got that.

Alright let's look

at this one, 4 is not equal

to the product of 2 and 3.

Hmm, a little tricky.

You see that word is again

but it's this whole part

that goes together,

4 is not equal so instead

of an equal sign we're gonna

use a not equal sign.

What's a not equal sign

look like?

Well, that's what an equal

sign looks like.

That's what a not equal sign

looks like.

You just put a slash

through it, not equal.

So now we've got the left side

of the equation is just the

number 4.

So we have 4 on the left side,

4 is not equal to

and on the right hand side we

have the product of 2 and 3.

Alright product

means multiplication.

So the product of 2

and 3 means we're gonna

multiply 2 times 3.

So we can just say 2 times 3

with a dot

or you could put a 2

parenthesis 3

to denote multiplication

and this makes sense.

Hopefully everybody,

4 is not equal to 6,

right cause 4

and 6 aren't the same number.

Notice there was no variable

in this one.

That's okay.

So this is still just taking a

statement and writing it using

the symbols.

In this case all the symbols

were just numbers

and the not equal sign.

Alright the sum of a number

in 8 is less than 14.

Again you see this word is

but you kind of have to look

at the context.

It says is less

than something.

So this time instead of is,

which would be equal,

we have is less than.

This symbol is written

like this, is less than.

So again we've broken

up what comes before

that is the sum of the number

in 8 and the sum, remember,

means addition.

So a number, we'll use n

and the other part of it is 8

so n plus 8 is less than,

right, what's

on the other side

of the equal sign, I'm sorry,

of the less than symbol, 14.

So now we've just translated

this sentence

into an inequality.

Both of these

on this page are called

inequalities

because they don't have just

an equal sign.

We've got a not equal sign

and we have a less

than symbol.

So these are called

inequalities as opposed

to equations

but they're still

algebraic inequalities.

I guess this first one is

actually just numerical,

there's no algebra.

So it's just an inequality

with numbers.

Alright here are a couple

for you to try on your own

and then we'll check them

so put the video on pause

and try these two.

Alright the first one,

4 decreased

by twice a number is 1 more

than the number.

Okay we've got just is this

time so that's gonna separate

the two parts.

So first we've got 4 decreased

by twice a number, hmm,

4 decreased by,

alright so I've got to start

with the number 4

and then I'm gonna decrease it

so I have to subtract

something from that.

What is it gonna be?

I'm subtracting twice a

number, that's 2 times n

so I write 2n.

And I've got is,

there's my equal.

Alright now we've got,

right hand side,

1 more than the number.

Alright 1 more

than something is I'm adding 1

to something.

What am I adding it to?

Whatever that number is,

same number,

n. So I've got 4 minus 2n

equals n plus 1.

So all we're doing

is translating.

We're not worrying

about what n is.

Alright and let's see this

last one, 3 times a number is

greater than or equal to 9,

hmm, tricky.

So I've got,

this whole part is greater

than or equal to,

that's this symbol,

greater than or equal to.

Alright so on the left hand

side of that I've got 3 times

the number,

on the right hand side I've

got 9.

So on the left hand side 3

times the number can be

written as 3n,

cause we're using n

to represent the number.

On the right side we've just

got the number 9

so now we've written 3n is

greater than or equal to 9.

So that's just a little

introduction

to translating some sentences

into equations

or inequalities.

Where there's an equal sign

it's an equation.

When you've got greater than

or a less than symbol or a not

to equal symbol,

then we're talking

about an inequality.

[ Silence ]