Question

given: ab = 3x + 2; bc = 4x + 8; ac = 38
prove: x = 4

statements	reason
2. ab + bc = ac	2. angle addition postulate
3. 3x + 2 + 4x + 8 = 38	3. substitution property of equality
4. 7x + 10 = 38	4. combining like terms
5. 7x = 28	5. subtraction property of equality
6. x = 4	6. division property of equality

on which line, did daniel make his error?

• line 3
• line 5
• line 2
• line 4

Explanation:

Step1: Analyze Line 2

The problem involves segments \(AB\), \(BC\), and \(AC\). The correct postulate for segment addition (when \(B\) is between \(A\) and \(C\)) is the Segment Addition Postulate, not the Angle Addition Postulate. So line 2 has an error in the reason.

Step2: Verify Other Lines

• Line 3: Substituting \(AB = 3x + 2\), \(BC = 4x + 8\), and \(AC = 38\) into \(AB + BC = AC\) is correct (Substitution Property).
• Line 4: Combining \(3x+4x = 7x\) and \(2 + 8=10\) to get \(7x + 10 = 38\) is correct (Combining Like Terms).
• Line 5: Subtracting 10 from both sides (\(7x+10 - 10=38 - 10\)) gives \(7x = 28\), which is correct (Subtraction Property of Equality).

Answer:

line 2