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Tell which statement is not true. 1. If x+2/x = 5+y/5, then 2/x = y/5 2. If x/3 = y/4,...

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novjb | (Level 1) Salutatorian

Posted July 24, 2013 at 8:10 PM via web

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Tell which statement is not true.

1. If x+2/x = 5+y/5, then 2/x = y/5

2. If x/3 = y/4, then x/y = 4/3

3. If x+3/4 = y/5, then x+3/y =4/5

4.If x-4/4 = 3-y/y, then x/4 = 3/y

 

 

 

2 Answers | Add Yours

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted July 25, 2013 at 2:22 AM (Answer #1)

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For each statement, use cross-multiplication and solve for x for both the "if" clause and the "then" clause.

Statement 1:
If (x + 2) / x = (5 + y) / 5, then 2 / x = y / 5
IF...
5(x + 2) = x(5 + y)
5x + 10 = 5x + xy
5x + 10 + (-5x) = 5x + xy + (-5x)
10 = xy
x = 10/y
THEN...
2 / x = y / 5
2 * 5 = x * y
10 = xy
x = 10/y
Statement 1 is true.

Statement 2:
If x / 3 = y / 4, then x / y = 4 / 3 
IF... 
x / 3 = y / 4
4 * x = 3 * y
4x = 3y
4x / 4 = 3y / 4
x = 3y / 4
THEN...
x / y = 4 / 3
3 * x = 4 * y 
3x = 4y
3x / 3 = 4y / 3
x = 4y / 3
Statement 2 is false.

Statement 3:
If (x + 3) / 4 = y / 5, then (x + 3) / y = 4 / 5 
IF...
5(x + 3) = 4 * y
5x + 15 = 4y
5x + 15 + (-15) = 4y + (-15)
5x = 4y - 15
5x / 5 = (4y - 15) / 5
x = 0.8y - 3
THEN...
(x + 3) / y = 4 / 5
5(x + 3) = 4 * y
5x + 15 = 4y
5x + 15 + (-15) = 4y + (-15)
5x = 4y - 15
5x / 5 = (4y - 15) / 5
x = 0.8y - 3
Statement 3 is true.

Statement 4:
If (x - 4) / 4 = (3 - y) / y, then x / 4 = 3 / y
IF...
(x - 4) / 4 = (3 - y) / y
y(x - 4) = 4(3 - y)
xy - 4y = 12 - 4y
xy - 4y + 4y = 12 - 4y + 4y
xy = 12
xy / y = 12 / y
x = 12 / y 
THEN...
x / 4 = 3 / y
x * y = 4 * 3
xy = 12
xy / y = 12 / y
x = 12 / y
Statement 4 is true.

The statement that is not true is STATEMENT 2.

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navam | eNotes Newbie

Posted July 25, 2013 at 2:31 AM (Answer #2)

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Answer is No.2.

Solution:

x/3=y/4

When cross multiplying, we get

x/y=3/4

Hence No.2 is not true.

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