Question

If M is the midpoint of AB, AM = 7x – 3, and MB = 5x + 7, then findthe value of x and the length of AB.7x-35x + 7X =The length of AB=units.

Answer 1

• x=5

,

• AB=64 units

Step-by-step explanation:

If M is the midpoint of AB, it means M divides AB into two equal parts, AM and MB.

Given:

• AM = 7x – 3

,

• MB = 5x + 7

`\begin{gathered} AM=MB \\ 7x-3=5x+7 \\ 7x-5x=7+3 \\ 2x=10 \\ x=5 \end{gathered}`

To find the length of AB, we first substitute x in AM.

`\begin{gathered} AM=7x-3 \\ =7(5)-3 \\ =35-3 \\ =32\text{ units} \end{gathered}`

Therefore:

`\begin{gathered} AB=AM*2 \\ =32*2 \\ =64\text{ Units} \end{gathered}`