Answer:
Step-by-step explanation:
To find the value of AC, we need to consider the relationships among the line segments in the given figure.
Given that BE = 2x + 2, BD = 5x - 3, and AE = 4x - 6, we can start by looking at the whole line segment AC.
AC can be expressed as the sum of AE and EC.
Therefore, AC = AE + EC.
Next, we need to find EC.
Since BE is a straight line, we have the equation BE = BD + DE.
This implies that EC = BD.
So, we can substitute EC = BD = 5x - 3 into the equation for AC.
Thus, AC = AE + BD = 4x - 6 + 5x - 3.
Combine like terms to simplify the expression:
AC = 4x - 6 + 5x - 3 = 9x - 9.
Answer: 11x - 7 + DC
Step-by-step explanation:
To find the length of AC, we can use the properties of triangles.
1. In triangle ABE, we have: - AE + BE = AB - Substituting the given values: - AB = (4x - 6) + (2x + 2) - AB = 6x - 4
2. In triangle BCD, we have: - BD + DC = BC - Substituting the given values: - BC = (5x - 3) + DC - BC = 5x - 3 + DC
3. As AC is a straight line, we know that AB + BC = AC: - AC = AB + BC - Substituting the values of AB and BC: - AC = (6x - 4) + (5x - 3 + DC) - AC = 11x - 7 + DC Therefore, the length of AC is represented as 11x - 7 + DC.