Question

suppose m is the mid - point of ab. if am = 6x - 3 and ab = 54, find the value of x and am.

Explanation:

Step1: Recall mid - point property

If $M$ is the mid - point of $AB$, then $AM=\frac{AB}{2}$.

Step2: Substitute given values

Given $AB = 54$, so $AM=\frac{54}{2}=27$.

Step3: Set up equation for $x$

Since $AM = 6x−3$ and $AM = 27$, we have the equation $6x−3=27$.

Step4: Solve for $x$

Add 3 to both sides: $6x=27 + 3=30$. Then divide both sides by 6: $x=\frac{30}{6}=5$.

Answer:

$x = 5$, $AM=27$