Question

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

Answer 1

Answer:

$x=2$

Step-by-step explanation:

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

$AB+BC=5(2x+2)$

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

$AB=BC$

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

$AB+BC=5(2x+2)$

This is equivalent to:

$AB+AB=5(2x+2)$

Combine like terms:

$2AB=5(2x+2)$

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

$2(3(3x-1))=5(2x+2)$

Now, solve for x.

Distribute the left side:

$6(3x-1)=5(2x+2)$

Distribute both sides:

$18x-6=10x+10$

Add 6 to both sides:

$18x=10x+16$

Subtract 10x from both sides:

$8x=16$

Divide both sides by 8:

$x=2$

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:

$AB=BC=3(3(2)-1)=15$

And the entire length AC is:

$AC=2(15)=30$

Answer 2

Answer:

$x=2$

Step-by-step explanation:

B is the midpoint of AC so AB = BC.

AB + BC = AC

AB + AB = AC

2(AB) = AC

$2\left(3\left(3x-1\right)\right)=5\left(2x+2\right)$

Expand:

$2\times3\left(3x-1\right)=5(2x+2)$

$6\left(3x-1\right)=5(2x+2)$

$6\times3x-6\times1=5\times2x+5\times2$

$18x-6=10x+10$

Add 6 to both sides:

$18x-6+6=10x+10+6$

$18x=10x+16$

Subtract 10x from both sides:

$18x-10x=10x+16-10x$

$8x=16$

Divide both sides by 8:

$\frac{8x}{8}=\frac{16}{8}$

$x=2$