Question

Points A,B, and M are collinear with M being the midpoint. Given that AM= 11x + 7 and MB= 8x + 22, solve for x.

Answer 1

To find the value of x for the collinear points A, B, and M with M as the midpoint, we set the given lengths AM and MB equal to each other. This results in the equation 11x + 7 = 8x + 22, which simplifies to x = 5.

Step-by-step explanation:

To solve for x when given that points A, B, and M are collinear with M being the midpoint, and the lengths AM and MB are given as AM = 11x + 7 and MB = 8x + 22, we use the property that the midpoint divides a line segment into two equal parts. Hence, AM must be equal to MB.

Setting the two expressions for AM and MB equal to each other, we get the equation:

1. 11x + 7 = 8x + 22

Next, we solve for x:

1. Subtract 8x from both sides to get 3x + 7 = 22.
2. Subtract 7 from both sides to get 3x = 15.
3. Divide both sides by 3 to get x = 5.