SAT algebra equation

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• Feb 14th 2011, 09:42 AM
vaironxxrd
SAT algebra equation
Hello Guys i was doing a Algebra SAT question.. and it was logical so i believe i got the right answer but in the future i don't want to get confuse so is there anyway to set an equation for this ?.

If 2x+2x+2x+2x=12 Then what is 2x-1=

I got that X is 2 because 2.2=4,2.2=4 2.2=4 =12 so 2.2-1=3

But i really don't know what would i ahve done if it was a bigger number..
• Feb 14th 2011, 09:45 AM
Ackbeet
$\underbrace{2x+2x+2x+2x}_{\text{Are there 3 or 4 of these?}}=12.$
• Feb 14th 2011, 09:45 AM
harish21
$2x+2x+2x+2x=12 \implies 8x=12 \implies x=\dfrac{12}{8}$

now find 2x-1
• Feb 14th 2011, 09:46 AM
Ackbeet
Incidentally, you're in the right forum.
• Feb 14th 2011, 09:51 AM
vaironxxrd
Quote:

Originally Posted by Ackbeet
$\underbrace{2x+2x+2x+2x}_{\text{Are there 3 or 4 of these?}}=12.$

I got the book home but i am pretty sure is 3 of them because when i got 12 the only answer could been 3, 4's
• Feb 14th 2011, 09:54 AM
vaironxxrd
$$\implies x=\dfrac{12}{8}$$ . You get 1.5
• Feb 14th 2011, 09:57 AM
Ackbeet
It makes a big difference if there are three or four of them. If there are three, then you're correct, and x = 2. You also correctly computed 2x-1, although your notation of using '.' for multiplication is not a good one for numbers. Use the asterisk: * for multiplication.

Quote:

But i really don't know what would i ahve done if it was a bigger number..
If what was a bigger number?
• Feb 14th 2011, 09:58 AM
DrSteve
The question should have $2x+2x+2x=12$.

Simple strategy: "Take a guess"

Try to take a reasonable guess for $x$. Let's try $x=3$. Then $2(3) + 2(3) + 2(3) = 6+6+6=18$, too big.

So let's try $x=2$. Then $2(2)+2(2)+2(2) = 4+4+4=12$. Just right.

So $x=2$ and $2x-1=2(2)-1=4-1=3$.

Note that you can do all of these computations quickly in your calculator.

After you're comfortable with the method of "guessing", also try to solve the problem algebraically.
• Feb 14th 2011, 10:01 AM
vaironxxrd
Quote:

Originally Posted by harish21
$2x+2x+2x+2x=12 \implies 8x=12 \implies x=\dfrac{12}{8}$

now find 2x-1

Quote:

Originally Posted by Ackbeet
It makes a big difference if there are three or four of them. If there are three, then you're correct, and x = 2. You also correctly computed 2x-1, although your notation of using '.' for multiplication is not a good one for numbers. Use the asterisk: * for multiplication.

If what was a bigger number?

if that 2 and the 12 where bigger, is there any Equation i could use?
• Feb 14th 2011, 10:02 AM
vaironxxrd
Quote:

Originally Posted by DrSteve
The question should have $2x+2x+2x=12$.

Simple strategy: "Take a guess"

Try to take a reasonable guess for $x$. Let's try $x=3$. Then $2(3) + 2(3) + 2(3) = 6+6+6=18$, too big.

So let's try $x=2$. Then $2(2)+2(2)+2(2) = 4+4+4=12$. Just right.

So $x=2$ and $2x-1=2(2)-1=4-1=3$.

Note that you can do all of these computations quickly in your calculator.

After you're comfortable with the method of "guessing", also try to solve the problem algebraically.

Yea i did it over the method of logic , and guessing
but im trying to find it algebraically now
• Feb 14th 2011, 10:04 AM
Ackbeet
Quote:

Originally Posted by vaironxxrd
if that 2 and the 12 where bigger, is there any Equation i could use?

Well, there's no equation. But there is a procedure:

$3x+3x+3x=21$

$9x=21$

$x=\dfrac{21}{9}=\dfrac{7}{3}.$

Then plug into your $2x-1$ expression to obtain

$2\left(\dfrac{7}{3}\right)-1=\dots$
• Feb 14th 2011, 10:08 AM
vaironxxrd
Quote:

Originally Posted by Ackbeet
Well, there's no equation. But there is a procedure:

$3x+3x+3x=21$

$9x=21$

$x=\dfrac{21}{9}=\dfrac{7}{3}.$

Then plug into your $2x-1$ expression to obtain

$2\left(\dfrac{7}{3}\right)-1=\dots$

I see you simplified the fraction So that would be 2*7 and 2*3 -1?
• Feb 14th 2011, 10:08 AM
Unknown008
If you know how to factorise, you can make it a little simpler.

2x + 2x + 2x + 2x = 12

x(2 + 2 + 2 + 2) = 12

What is 2 + 2 + 2 + 2? It's 8 of course!

Then, x*8 = 12

x = 12/8 = 1.5

You can apply the same procedure for bigger numbers.
• Feb 14th 2011, 10:09 AM
Ackbeet
Quote:

Originally Posted by vaironxxrd
I see you simplified the fraction So that would be 2*7 and 2*3 -1?

No, no. You multiply the scalar 2 times the fraction 7/3. THEN you add the fractions by getting a common denominator.
• Feb 14th 2011, 10:09 AM
vaironxxrd
Quote:

Originally Posted by Unknown008
If you know how to factorise, you can make it a little simpler.

2x + 2x + 2x + 2x = 12

x(2 + 2 + 2 + 2) = 12

What is 2 + 2 + 2 + 2? It's 8 of course!

Then, x*8 = 12

x = 12/8 = 1.5

You can apply the same procedure for bigger numbers.

yea it is 1.5 But if you do 2*1.5 you get 3 not 2*1.5-1
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