Question

1. find x if ac = 19x, ab = 9x, and bc = 10.
2. find x if ab = x + 2, bc = 2x - 7 and ac = 22.
3. bc = x + 12, ac = 16, and ab = 18 + x. find x.
4. find x if ac = 8, ab = 2x - 18, and bc = 2x - 14.

find the length indicated.

1. find lk

diagram: line segment m---l---k, ml = 56 + x, lk = 2x + 17, total length 12

1. find eg

diagram: line segment e---f---g, ef = 10x, fg = 3, total eg = 14x - 1

1. find vw

diagram: line segment u---v---w, uv = 19, vw = 30 + 2x, total uw = x + 28

1. find dc

diagram: line segment d---c---b, dc = 19 + x, cb = x + 24, total db = 19

Explanation:

Let's solve problem 5 first:

Step1: Assume points A, B, C are colinear with B between A and C, so \( AC = AB + BC \)

\( 19x = 9x + 10 \)

Step2: Subtract \( 9x \) from both sides

\( 19x - 9x = 10 \)
\( 10x = 10 \)

Step3: Divide both sides by 10

\( x = \frac{10}{10} = 1 \)

#[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]

Answer:

Step1: Assume points A, B, C are colinear with B between A and C, so \( AC = AB + BC \)

\( 19x = 9x + 10 \)

Step2: Subtract \( 9x \) from both sides

\( 19x - 9x = 10 \)
\( 10x = 10 \)

Step3: Divide both sides by 10

\( x = \frac{10}{10} = 1 \)

#[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]