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].
