I need help on this mathematical equation B is the Midpoint of AC.

Step-by-step explanation:

B is the midpoint of AC so AB = BC.

AB + BC = AC

AB + AB = AC

2(AB) = AC

Expand:

Add 6 to both sides:

Subtract 10x from both sides:

Divide both sides by 8:

Step-by-step explanation:

First, we know that the entire segment adds up to 5(2x+2). In other words:

Now, since B is the midpoint of AC, by the definition of midpoint, AB and BC are equivalent. So:

Since we know that, let's substitute BC for AB in the first equation:

This is equivalent to:

Combine like terms:

And since we know that AB is 3(3x-1), substitute:

Now, solve for x.

Distribute the left side:

Distribute both sides:

Add 6 to both sides:

Subtract 10x from both sides:

Divide both sides by 8:

So, the value of x is 2.

And we're done!

Notes:

You didn't particularly state what you need to find. If you want to length of AB or BC, it would be:

And the entire length AC is:

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step-by-step explanation: