Question

step 1 plot two points and a and c. connect the points
step 2 plot point b between points and c.
step 3 label segments ab, bc, and
step 4 use betweenness of points to
ac = ab + bc
4x - 12 = x + 2x + 3
4x - 12 = ____x + 3
x - 12 = ____
x = ____
now find bc.
bc = 2x + 3
= 2(____) + 3
= ____

Explanation:

Step1: Combine like - terms on the right - hand side

Combine $x$ and $2x$ in the equation $4x - 12=x + 2x+3$.
$4x - 12 = 3x+3$

Step2: Isolate the variable terms

Subtract $3x$ from both sides of the equation $4x - 12 = 3x+3$.
$4x-3x - 12=3x - 3x+3$
$x - 12 = 3$

Step3: Solve for $x$

Add 12 to both sides of the equation $x - 12 = 3$.
$x-12 + 12=3 + 12$
$x = 15$

Step4: Find the length of $BC$

Substitute $x = 15$ into the expression for $BC$ which is $BC = 2x+3$.
$BC=2\times15 + 3$
$BC = 30+3$
$BC = 33$

Answer:

The blanks are filled as follows:
$4x - 12=\underline{3}x + 3$
$x - 12=\underline{3}$
$x=\underline{15}$
$BC = 2(\underline{15})+3$
$BC=\underline{33}$