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Mathematics 8 Online
OpenStudy (anonymous):

How many solutions does the equation have? 2(2x+5)=4(x+3) A. one solution B. infinite solutions C. no solution

OpenStudy (solomonzelman):

2(2x+5)=4(x+3) 4x+10=4x+12

OpenStudy (solomonzelman):

Is that true for any values of x?

OpenStudy (anonymous):

no solution?

OpenStudy (solomonzelman):

Yes

OpenStudy (anonymous):

Thank You!

OpenStudy (solomonzelman):

Yw !

OpenStudy (anonymous):

How many solutions does the equation have? a+5=1/5(5a+25) A. one solution B. infinite solutions C. no solution What about this one i think infinite solutions

OpenStudy (solomonzelman):

\(\large\color{black}{ a+5=\frac{1}{5}(5a+25)}\) like this?

OpenStudy (anonymous):

yes

OpenStudy (solomonzelman):

then you are correct - "infinte solutions" is the right answer.

OpenStudy (solomonzelman):

Because when you expand the right side, you get: \(\large\color{black}{ a+5=\frac{1}{5}(5a+25)}\) \(\large\color{black}{ a+5=a+5}\) and that is true for any value of a.

OpenStudy (anonymous):

Thank you again!

OpenStudy (solomonzelman):

You welcome, again! :)

OpenStudy (anonymous):

I have 3 more

OpenStudy (anonymous):

if you could check them

OpenStudy (solomonzelman):

Alright...

OpenStudy (anonymous):

How many solutions does the equation have? 4x + 2(x-3)=8x + 12 A. one solution B. infinite solutions C. no solution

OpenStudy (solomonzelman):

what did you choose?

OpenStudy (anonymous):

A?

OpenStudy (solomonzelman):

Yes, correct!

OpenStudy (anonymous):

Thank You!!

OpenStudy (solomonzelman):

yw

OpenStudy (anonymous):

Which expressions would complete this equation so that it has infinitely many solutions? 8 + 2(8x – 6) = Choose exactly two answers that are correct. A. 2(4x + 7) B. 9x – 10 C. 16x – 4 D. 4(4x – 1)

OpenStudy (solomonzelman):

and your choice was?

OpenStudy (anonymous):

C and D?

OpenStudy (anonymous):

Or A and D?

OpenStudy (solomonzelman):

8 + 2(8x – 6) = 8 + 16x – 12 = 16x – 4. ` same = same ` ----> ` 8 + 2(8x – 6) = 16x - 4 ` C is right

OpenStudy (anonymous):

So C and D?

OpenStudy (solomonzelman):

8 + 2(8x – 6) = 8 + 4(4x – 3) = 8 + 4(4x – 1 - 2) = 8 + 4(4x – 1) + (-2)(4) = 8 + 4(4x – 1) -8 = 4(4x – 1) =

OpenStudy (solomonzelman):

yes, C and D

OpenStudy (anonymous):

Thanks Again!!! I have one more

OpenStudy (solomonzelman):

k

OpenStudy (anonymous):

What is the best way to classify each equation? Column AColumn B 1. 8x + 24=2(4x+12) 2. 5x + 18-x=2(2x+8) 3. 7(3x-2)=20x-13 4. 3x + 2(x-10)=5(x-4) A. identity B. contradiction C. neither @SolomonZelman

OpenStudy (solomonzelman):

Can you write the Columns more clearly please?

OpenStudy (anonymous):

dont worry about the columns... Column A is with the long equations and Column B is A. identity B. contradiction C. neither

OpenStudy (solomonzelman):

Column A Column B 1. 8x + 24=2(4x+12) 2. 5x + 18-x=2(2x+8) 3. 7(3x-2)=20x-13 4. 3x + 2(x-10)=5(x-4) like this?

OpenStudy (anonymous):

what you have underneath column B is suppose to be under Column A and under Column B is suppose to be this A. identity B. contradiction C. neither

OpenStudy (solomonzelman):

Column A Column B 8x+24=2(4x+12) Identity 5x+18-x=2(2x+8) Contradiction 7(3x-2)=20x-13 Niether 3x+2(x-10)=5(x-4) like this?

OpenStudy (anonymous):

yes

OpenStudy (solomonzelman):

`(When you expand 1st row, 1st column)` 8x+24=2(4x+12) \(\longrightarrow\) 8x+24=8x+24

OpenStudy (solomonzelman):

`(Expand 2nd row, 1st column)` 5x+18-x=2(2x+8) \(\longrightarrow\) 5x+18-x=4x+16 `(Subtract x from 5x: 5x-x=4x)` 5x+18-x=4x+16 \(\longrightarrow\) 4x+18=4x+16

OpenStudy (solomonzelman):

So at this point you should be able to tell me whether A is an *identity* (true for all values of x), a *contradiction* (true for NO values of x - i.e. always false) OR *Niether* (not contradition or identity - i.e. has 1 solution)

OpenStudy (solomonzelman):

`(Expand 3rd row, 1st column)` 7(3x-2)=20x-13 \(\longrightarrow\) 21x-14=20x-13 `(Subtract 20x from both sides)` 21x-14=20x-13 \(\longrightarrow\) x-14=13 `(Add 14 to both sides)` x-14=13 \(\longrightarrow\) x=27 (and this is Niether)

OpenStudy (solomonzelman):

`(Expand 4th row, 1st column)` 3x+2(x-10)=5(x-4) \(\longrightarrow\) 3x+2x-20=5x-20 `(Add like terms on the left side)` 3x+2x-20=5x-20 \(\longrightarrow\) 5x-20=5x-20 Can you identify this one as either: *identity*, *contradiction*, or *Neither*

OpenStudy (anonymous):

sorry I had to leave but im back @SolomonZelman

OpenStudy (solomonzelman):

Ok, read over my posts, please. This should clarify every thing....

OpenStudy (anonymous):

ok

OpenStudy (anonymous):

so 1.A 2.B. 3.C 4.A?

OpenStudy (solomonzelman):

yes, Identity Contradition Neither Identity *CORRECT!*

OpenStudy (anonymous):

THANK YOU!!!!!!!

OpenStudy (solomonzelman):

Anytime:)

OpenStudy (anonymous):

I got 100%

OpenStudy (solomonzelman):

Nice to hear that:)

OpenStudy (solomonzelman):

have a good night!

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