Final answer:
To find the value of x, set up the equation (2x+7 + 6x-57)/2 = 15 and solve for x. The value of x is 10.
Step-by-step explanation:
To find the value of x, we can use the fact that the median of a trapezoid is equal to the average of the two bases. Given that the median is 15 centimeters and the bases have lengths of 2x+7 and 6x-57, we can set up the equation: (2x+7 + 6x-57)/2 = 15. Solving this equation will give us the value of x.
First, we simplify the equation by combining like terms: 8x-50 = 30. Next, we isolate the variable by adding 50 to both sides: 8x = 80. Finally, we solve for x by dividing both sides by 8: x = 10.
Therefore, the value of x is 10.