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equation is not equivalent to the others










































Which equation is not equivalent to the others?

zero point four x equals one point two

six x equals eighteen

two x equals zero point six

x equals three

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Mar 24, 2014
not equivalent
by: Staff


Answer

Part I

Which equation is not equivalent to the others?

zero point four x equals one point two

six x equals eighteen

two x equals zero point six

x equals three



Which equation is not equivalent to the others ?




The first thing to do is to translate the words into mathematical symbols.


1st equation: English Language Version

zero point four x equals one point two

the translation to mathematical symbols:


"zero" can be replaced with the number: 0

"point" can be replaced with a decimal point: .

"four" can be replaced with the number: 4

x is the unknown. Just leave it as x.

"equals" can be replaced with the equal sign: =

"one" can be replaced with the number: 1

"point" can be replaced with a decimal point: .

"two" can be replaced with the number: 2

the final equation, using mathematical symbols instead of words:

0.4x = 1.2




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Mar 24, 2014
not equivalent
by: Staff


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Part II

2nd equation: English Language Version

six x equals eighteen

the translation to mathematical symbols:

"six" can be replaced with the number: 6


x is the unknown. Just leave it as x.

"equals" can be replaced with the equal sign: =

"eighteen" can be replaced with the number: 18


the final equation, using mathematical symbols instead of words:

6x = 18



3rd equation: English Language Version

two x equals zero point six

the translation to mathematical symbols:

"two" can be replaced with the number: 2

x is the unknown. Just leave it as x.

"equals" can be replaced with the equal sign: =

"zero" can be replaced with the number: 0

"point" can be replaced with a decimal point: .

"six" can be replaced with the number: 6

the final equation, using mathematical symbols instead of words:

2x = 0.6



4th equation: English Language Version

x equals three

the translation to mathematical symbols:


x is the unknown. Just leave it as x.


"equals" can be replaced with the equal sign: =

"three" can be replaced with the number: 3


the final equation, using mathematical symbols instead of words:

x = 3


the four equations, expressed in mathematical symbols, are:

zero point four x equals one point two: 0.4x = 1.2

six x equals eighteen: 6x = 18

two x equals zero point six: 2x = 0.6

x equals three: x = 3







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Mar 24, 2014
not equivalent
by: Staff


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Part III


Translate the words into mathematical symbols.




What does the term "equivalent" actually mean?

There is a difference between equivalent values, equivalent expressions, and equivalent equations.


Here are some examples:

Equivalent values:

The value of 500 pennies is equivalent to the value of a $5 bill. Both have the same purchasing power. You can purchase an item costing five dollars with a $5 bill, or with 500 pennies.

A distance of 5 ½ feet is equivalent to 66 inches.

1 hour is equivalent to 60 minutes, or 3600 seconds.


Equivalent expressions:

Equivalent expressions are not equations.

3(x^2 + 1) and 3x^2 + 3 are equivalent expressions regardless of what the value of x turns out to be.


Equivalent equations:


(x + 5)^3 = 0 and x = -5 are equivalent equations. (However, (x + 5)^3 and x are definitely not equivalent expressions for all values of x.)



Equivalent equations will always have the same solution.

The easiest way to find out which equation is not equivalent to the others is to solve for the value of x in all four equations.

When the value of x in three of the equations is the same, and the value of x in the "other equation" is a different value, the "other equation" is the answer.



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Mar 24, 2014
not equivalent
by: Staff


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Part IV



(1) solve for x in all four equations, and then (2) compare the values  to find out which equation is not equivalent to the others





Solve for x in each equation:

1st equation: zero point four x equals one point two: 0.4x = 1.2

solve for x by dividing each side of the equation by 0.4

0.4x = 1.2

(0.4x = 1.2) / 0.4

0.4x / 0.4 = 1.2 / 0.4

(0.4 / 0.4) * x = (3 * 0.4) / 0.4

(0.4 / 0.4) * x = 3 * (0.4 / 0.4)

(1) * x = 3 * (1)

x = 3 for the equation 0.4x = 1.2




solve the first equation for x:  part A








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Mar 24, 2014
not equivalent
by: Staff


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Part V


solve the first equation for x:  part B





2nd equation: six x equals eighteen: 6x = 18

solve for x by dividing each side of the equation by 6

6x = 18

(6x = 18) / 6

6x / 6 = 18 / 6

(6 / 6) * x = (3 * 6) / 6

(6 / 6) * x = 3 * (6 / 6)

(1) * x = 3 * (1)

x = 3 for the equation 6x = 18



solve the second equation for x:  part A






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Mar 24, 2014
not equivalent
by: Staff


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Part VI



solve the second equation for x:  part B





4th equation: x equals three


x = 3 for the equation x = 3



solve the fourth equation for x






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Mar 24, 2014
not equivalent
by: Staff


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Part VII


3rd equation: two x equals zero point six: 2x = 0.6

solve for x by dividing each side of the equation by 2

2x = 0.6

(2x = 0.6) / 2

2x / 2 = 0.6 / 2

(2 / 2) * x = (0.3 * 2) / 2

(2 / 2) * x = 0.3 * (2 / 2)

(1) * x = 0.3 * (1)

x = 0.3 for the equation 2x = 0.6



solve the third equation for x:  part A




solve the third equation for x:  part B






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Mar 24, 2014
not equivalent
by: Staff


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Part VIII


Final Answer:

2x = 0.6 is not equivalent to the other equations




The equation which is not equivalent to the others.




It is also worth noting that the three equivalent equations (0.4x = 1.2, 6x = 18, and x = 3) are also dependent equations.

Each of the three equations can be derived from either of the other two equations.


Three equivalent equations which are also dependent equations.







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Mar 24, 2014
not equivalent
by: Staff


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Part IX



dependent equations:  equations which can be derived from the other dependent equations in the system.




The second equation (6x = 18) can be derived by multiplying the first equation (0.4x = 1.2) by 15.

0.4x = 1.2, first equation

15 * (0.4x = 1.2)

15 * 0.4x = 15 * 1.2

6x = 18, second equation



Likewise, the first equation (0.4x = 1.2) can be derived by dividing the second equation (6x = 18) by 15.

6x = 18, second equation

(6x = 18) / 15

6x /15 = 18 / 15

(2 * 3)x / (5 * 3) = (3 * 6) / (3 * 5)

(2 / 5) * (3 / 3) * x = (3 / 3) * (6 / 5)

(2 / 5) * (1) * x = (1) * (6 / 5)

(2 / 5) * x = (6 / 5)

(0.4) * x = (1.2)

0.4x = 1.2, first equation




As already shown above, the equation (x = 3) can be derived by dividing the first equation (0.4x = 1.2) by 0.4.

It can also can also be derived by dividing the second equation (6x = 18) by 6.




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Mar 24, 2014
not equivalent
by: Staff


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Part X


dependent equations:  verifying the dependency





The other equation (2x = 0.6) cannot be derived from any of the other equations.

Again, the answer to your question is: 2x = 0.6 is not equivalent to the other equations


independent equation (2x = 0.6) cannot be derived from any of the other equations







Thanks for writing.

Staff
www.solving-math-problems.com


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