Question

If B is the midpoint of AC, and AC=8x-20, find BC.​

Answer 1

2(3x-1)=8x-20
SIMPLY

6x-2=8x-20
SUBTRACT 6x ON BOTH SIDES

-2=2x-20
ADD 20 TO BOTH SIDES

18=2x
DIVIDE 2 ON BOTH SIDES

X=9
SUBSTITUTE

3(9)-1

27-1

26

BC=26

Answer 2

Answer:

$BC=26$

Step-by-step explanation:

Start with:

$AB+BC=AC$

Since $B$ is the midpoint, we also know that:

$AB=BC$

Knowing this, we can use a system of equations and substitute $AB$ for $BC$ in the equation we started with:

$AB+AB=AC$

Let's identify our values:

$AB=3x-1\\AC=8x-20$

Substitute:

$3x-1+3x-1=8x-20$

Combine like terms:

$6x-2=8x-20$

Add $20$ to both sides of the equation:

$6x+18=8x$

Subtract $6x$ from both sides of the equation:

$18=2x$

Divide by the coefficient of $x$, which is $2.$

$x=9$

Substitute $9$ into $3x-1$

$3(9)-1$

Solve:

$AB=26$

Remember that $AB=BC$, thus:

$BC=26$