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If [tex]$DE = 2x$[/tex], [tex]$EF = x - 2$[/tex], and [tex][tex]$DF = 10$[/tex][/tex], what is [tex]$DE$[/tex]?

Simplify your answer and write it as a proper fraction, mixed number, or integer.
[tex]$\square$[/tex]

Sagot :

GinnyAnsweridn
To solve the problem, we need to determine the value of [tex]\( DE \)[/tex].

We are given the following relationships:
- [tex]\( DE = 2x \)[/tex]
- [tex]\( EF = x - 2 \)[/tex]
- [tex]\( DF = 10 \)[/tex]

Since [tex]\( DF \)[/tex] represents the total distance from [tex]\( D \)[/tex] to [tex]\( F \)[/tex], we can express this as the sum of [tex]\( DE \)[/tex] and [tex]\( EF \)[/tex]. Therefore, we have the equation:
[tex]\[ DE + EF = DF \][/tex]

Substituting the given expressions for [tex]\( DE \)[/tex] and [tex]\( EF \)[/tex], we get:
[tex]\[ 2x + (x - 2) = 10 \][/tex]

Now, let's simplify and solve for [tex]\( x \)[/tex]:
[tex]\[ 2x + x - 2 = 10 \][/tex]
[tex]\[ 3x - 2 = 10 \][/tex]
[tex]\[ 3x = 12 \][/tex]
[tex]\[ x = 4 \][/tex]

Now that we have [tex]\( x \)[/tex], we can find [tex]\( DE \)[/tex] by substituting [tex]\( x \)[/tex] back into the expression for [tex]\( DE \)[/tex]:
[tex]\[ DE = 2x = 2 \times 4 = 8 \][/tex]

Therefore, the value of [tex]\( DE \)[/tex] is [tex]\( \boxed{8} \)[/tex].
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