Question

segment addition postulate practice
find de.
d 3x - 28 e 3x - 30 f x g
33
de = units

Explanation:

Step1: Apply segment - addition postulate

According to the segment - addition postulate, $DG=DE + EF+FG$. So, $(3x - 28)+(3x - 30)+x=33$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms, we get $(3x+3x + x)+(-28-30)=33$, which simplifies to $7x-58 = 33$.

Step3: Solve for $x$

Add 58 to both sides of the equation: $7x-58 + 58=33 + 58$, so $7x=91$. Then divide both sides by 7: $x=\frac{91}{7}=13$.

Step4: Find $DE$

Since $DE = 3x-28$, substitute $x = 13$ into the expression for $DE$. So, $DE=3\times13-28=39 - 28=11$.

Answer:

11