M is the midpoint of segment AB, AM=2x+4 and AB=12x+4. What is the value of MB? Show your work for credit.
I don't need the credit, you do.
If M is the midpoint, AM must equal MB, and both must be half of AB. Tey tell you that AB = 12x = 4.
Therefore 2x + 4 = 6x + 2
Solve for x and complete the problem.
They tell you that AB = 12x + 4.
Therefore 2x + 4 = 6x + 2
x = 0.5
AM = MB = 5
To find the value of MB, we need to use the definition of a midpoint, which states that the midpoint of a line segment divides it into two equal parts.
Given that M is the midpoint of segment AB, we can set up the equation:
AM + MB = AB
Plugging in the given values:
2x + 4 + MB = 12x + 4
Now, we can solve for MB by isolating it on one side of the equation:
MB = 12x + 4 - 2x - 4
Simplifying the right side of the equation:
MB = 10x
So, the value of MB is 10x.
To find the value of MB, we need to use the definition of a midpoint: the midpoint of a line segment is equidistant from both endpoints.
Given that M is the midpoint of segment AB, we can set up an equation using the definition above:
AM = MB
Now, substitute the given values into the equation:
2x + 4 = MB
Next, we need to determine the value of x. We can do this by comparing the lengths of AM and AB:
AM = AB/2
Substitute the given values into the equation:
2x + 4 = (12x + 4)/2
To simplify, multiply each term by 2 to get rid of the fraction:
4x + 8 = 12x + 4
Now, let's isolate x by moving the terms involving x to one side of the equation:
4x - 12x = 4 - 8
-8x = -4
Divide both sides of the equation by -8 to find the value of x:
x = -4/-8
x = 1/2
Now, substitute the value of x back into the equation AM = MB:
2(1/2) + 4 = MB
1 + 4 = MB
MB = 5
Therefore, the value of MB is 5.