Final answer:
To find the value of x in the equation 2x + 6 = 24, we set up the equation based on the given information. By subtracting 6 from both sides and dividing by 2, we find that x is equal to 9.
Step-by-step explanation:
To solve the problem, we can set up an equation using the given information. Since segment GK is bisected at point M, GM is equal to MK. Therefore, GM = MK = 2x + 6. We also know that GK is equal to 24. Setting up the equation, we have 2x + 6 = 24. By subtracting 6 from both sides and then dividing by 2, we can solve for x.
2x + 6 = 24
2x = 18
x = 9
The value of x, when segment GK bisected at point M with GM = 2x+6 and GK = 24, is 3.
In Mathematics, specifically in geometry, the phrase 'segment GK is bisected at point M' means that point M is the midpoint of the segment and therefore, GM (segment from G to M) equals MK (segment from M to K). Given that GM = 2x+6 and GK = 24, you can establish the equation 2x+6 = 24/2 because when a line is bisected, the two segments it produces are equal in length. Solving this equation, 2x+6 = 12, we subtract 6 from both sides to get 2x = 6. Then dividing both sides by 2, we find x = 3.
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