Final answer:
The student's question in Mathematics involves finding the value of x and the length AC, given that M is the midpoint of AC. By setting the expressions for AM and MC equal and solving for x, we find that x = 7 and thus the total length AC = 56 units.
Step-by-step explanation:
The question involves using the properties of a midpoint and solving an algebraic equation. Since M is the midpoint of AC, the segment lengths of AM and MC are equal. Thus, we can set AM equal to MC to find the value of x. The equation would be x + 21 = 5x - 7. Solving this equation for x, we get:
- x + 21 = 5x - 7
- Subtract x from both sides: 21 = 4x - 7
- Add 7 to both sides: 28 = 4x
- Divide by 4: x = 7
Once we have x = 7, we can substitute this value back into the expressions for AM or MC to find their lengths, which would be the same since M is the midpoint:
The length of AC, being double that of AM or MC since M is the midpoint, is 56 units.