Answer: The answer is: " x = 2.833333333333...." .
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or: write as: " 2 [tex]\frac{5}{6}[/tex] " .
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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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→ [tex]\frac{(x+3.5) }{20 } = \frac{(x-4) }{5}[/tex] ;
Now; "cross-factor multiply" :
→ [tex]\frac{a}{b} = \frac{c}{d }[/tex] ; → [tex]ad = bc[/tex] ; { [tex]{ a\neq0 ; b\neq0 ; c\neq0 ; d\neq0[/tex] .}.
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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 [tex]\frac{5}{6}[/tex] ."
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Hope this is helpful to you! Best wishes!
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