How do you use cross products to solve #3/4=x/(x+3)#?

Answer 1

#x=9#

#3/4=x/(x+3)# or #4x=3x+9# or #4x-3x=9# or #x=9#
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Answer 2

x = 9

To use cross products or #color(blue)"cross multiplication"# as it is also named.
#color(red)(3)/color(blue)(4)=color(blue)(x)/color(red)(x+3)#
now multiply the terms in #color(blue)("blue")" and "color(red)("red")# (X) and equate them.
#rArrcolor(blue)(4x)=color(red)(3(x+3))#

distribute the bracket : 4x = 3x + 9

subtract 3x from both sides to solve for x

#4x-3x=cancel(3x)+9cancel(-3x)rArrx=9#
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Answer 3

This is why the cross product works!!!

The cross product is a shortcut that bypasses some stages in solving by first principles. I will use first principles so you can see where the shortcut takes over.

A fraction is split up into two parts. Using descriptive but #ul("unconventional names")# we have #("count")/("size indicator")#
When you wish to #ul(directly")# compare quantities the "size indicators" have to be the same. This is also true for fractional addition and subtraction. You can not #ul("directly")# apply addition or subtraction unless the "size indicators" are the same.
#" "("count")/("size indicator") ->("numerator")/("denominator")# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Solving your question")#
Using a 'common denominator' of #4(x+3)#
#color(brown)([3/4xx1]=[x/(x+3)xx1]color(blue)(""->""[3/4xx(x+3)/(x+3) ]=[x/(x+3)xx4/4]#
#(3(x+3))/(4(x+3)) = (4x)/(4(x+3))#

If you look at the numerators you will see the result you get by the short cut

Multiply both sides by #4(x+3)# and you end up with
#3(x+3)=4x" "larr" the consequences of the shortcut"#
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Answer 4

To solve ( \frac{3}{4} = \frac{x}{x+3} ) using cross products:

  1. Multiply both sides of the equation by ( x+3 ).
  2. This yields: ( 3(x+3) = 4x ).
  3. Expand and simplify the equation: ( 3x + 9 = 4x ).
  4. Subtract ( 3x ) from both sides: ( 9 = x ).

Therefore, ( x = 9 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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