Question

1. if m is the midpoint of segment ab and if am = 6x - 8 and mb = 3x + 19, find mb.

Explanation:

Step1: Set AM equal to MB (midpoint property)

Since M is the midpoint of AB, \( AM = MB \). So we set up the equation:
\( 6x - 8 = 3x + 19 \)

Step2: Solve for x

Subtract \( 3x \) from both sides:
\( 6x - 3x - 8 = 3x - 3x + 19 \)
\( 3x - 8 = 19 \)

Add 8 to both sides:
\( 3x - 8 + 8 = 19 + 8 \)
\( 3x = 27 \)

Divide both sides by 3:
\( \frac{3x}{3} = \frac{27}{3} \)
\( x = 9 \)

Step3: Substitute x into MB's expression

Now that we have \( x = 9 \), substitute it into \( MB = 3x + 19 \):
\( MB = 3(9) + 19 \)
\( MB = 27 + 19 \)
\( MB = 46 \)

Answer:

46