3. A, B, and mathrm{C} are collinear points with mathrm{B} being the midpoint of overline{A C}. If A B=2 x+1 and B C=3 x-4, then find A C.

Question

Accepted Answer

Step:1 ：Given that B is the midpoint of AC, it means that AB = BC.Step:2 ：Set up the equation (2x + 1 = 3x - 4) to solve for x.Step:3 ：Solving the equation gives x = 5.Step:4 ：Substitute x = 5 into either AB = 2x + 1 or BC = 3x - 4 to find the length of AB or BC. This gives AB = BC = 11.Step:5 ：Since AB = BC, the length of AC would be 2 * AB or 2 * BC, which gives AC = 22.Step:6 ：Final Answer: The length of AC is (boxed{22}).

Answer

Step: 1 ：Given that B is the midpoint of AC, it means that AB = BC.Step: 2 ：Set up the equation (2x + 1 = 3x - 4) to solve for x.Step: 3 ：Solving the equation gives x = 5.Step: 4 ：Substitute x = 5 into either AB = 2x + 1 or BC = 3x - 4 to find the length of AB or BC. This gives AB = BC = 11.Step: 5 ：Since AB = BC, the length of AC would be 2 * AB or 2 * BC, which gives AC = 22.Step: 6 ：Final Answer: The length of AC is (boxed{22}).

3. A, B, and $\mathrm{C}$ are collinear points with $\mathrm{B}$ being the midpoint of $\overline{A C}$. If $A B=2 x+1$ and $B C=3 x-4$, then find $A C$.

Answer

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