Question

b) if $eb = 2x + 8, db = 3x - 8$, find $ed$.

Explanation:

Step1: Observe the figure for a relationship

Since the segments are related in a way that \(EB = ED+DB\) and from the figure's markings, we can assume \(ED = DB\).

Step2: Set up an equation

Set \(ED = DB\), so \(2x + 8=3x - 8+(3x - 8)\) (because \(EB = ED + DB\) and \(ED = DB\)). But a simpler way is to just set \(2x + 8=2(3x - 8)\) since \(EB = 2DB\).
\[2x+8 = 6x-16\]

Step3: Solve for \(x\)

Subtract \(2x\) from both sides:
\[8=6x - 2x-16\]
\[8 = 4x-16\]
Add 16 to both sides:
\[8 + 16=4x\]
\[24 = 4x\]
Divide both sides by 4:
\[x = 6\]

Step4: Find \(DB\)

Substitute \(x = 6\) into the expression for \(DB\): \(DB=3x - 8=3\times6 - 8=18 - 8 = 10\)

Step5: Find \(ED\)

Since \(ED = DB\), \(ED = 10\)

Answer:

10