Find the value of x that makes AFGH~AJKL.
(Lesson 11.3) (1 point)
X+3.5
20

 The answer is:  " x = 2.833333333333...." .

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             or:  write as:  " 2 " .  

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Step-by-step explanation:

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Set up a ratio:

Note:  Segment FH =  (x + 35)

         Segment JL = 20 ;

         Segment FH ~ Segment JL ;

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Note:  Segment GH = (x - 4) ;

         Segment  KL  =  5 ;

         Segment GH ~ Segment KL .

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So, ( x + 3.5) : 20 :: (x-4) : 5 ;

Write this ratio in fraction format:

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→    ;

Now; "cross-factor multiply" :

→    ;  → ; { .}.

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So:

  5(x + 3.5)  =  20(x - 4) ;  

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→ To simplify, start by divide each side of the equation by "5" ;

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  →   {5(x + 3.5) } / 5  =  { 20(x - 4)  } / 5 ;

to get:

      →  (x + 3.5)  =  4(x - 4) ;

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Now, on the right-hand side of the equation;

  let us expand the expression;

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We have the expression:  " 4(x - 4) " ;

 To expand:

Note the "distributive property of multiplication:

     →   a(b + c)  = ab + ac ;

Likewise:

     →   4(x - 4)  = 4x  - 16 ;

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Now, we can rewrite our equation:

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     →   " x + 3.5  =  4x - 15 "  ;

Now, we can subtract "x" from each side of the question;

     & add "15" to each side of the equation; as folllows:

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     →     x + 3.5  =  4x - 15 ;

          - x + 15   =  - x  +15

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to get:        8.5  =  3x ;  

                   ↔  3x  = 8.5 ;

Now, divide each side of the equation by "3" ;

       to isolate "x" on one side of the equation;

       & to solve for "x" ;  as follows:

                     →  3x / 3 = 8.5 / 3 ;

             to get:   x  = 8.5 /3  

                              = 2.83333333333 ;  

                         or; write as:  " 2 ."

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Hope this is helpful to you!  Best wishes!

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560

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