Question

M is between A and B and M is the midpoint of AB. If AM=3x-1 and Ab=40, Find x and BM?

Option 1: x = 10, BM = 21
Option 2: x = 5, BM = 15
Option 3: x = 7, BM = 20
Option 4: x = 15, BM = 5

Answer 1

After setting up an equation based on the midpoint, solving for x gives the value 7, and since AM is 20, BM is also 20.

Step-by-step explanation:

The question involves finding the value of x and the length of BM given that M is the midpoint of line AB, and we are provided with the expressions for the lengths of AM and AB. Since M is the midpoint, AM is equal to BM. We use this information to set up an equation with the given expression AM = 3x - 1 and the known length AB = 40.

To solve for x, we realize that AM is half of AB, so AM = BM = AB/2 = 40/2 = 20. Substituting AM = 20 into the expression AM = 3x - 1 and solving for x gives us:

20 = 3x - 1

21 = 3x

x = 7

Now we have the value of x, and since BM = AM = 20, we can determine that BM = 20. Therefore, the correct option is Option 3: x = 7, BM = 20.