Question

find the value. ab = x, and bc = 2x + 3. step 1 plot two points and label them a and c. connect the points. step 2 plot point b between points a and c. step 3 label segments ab, bc, and ac. step 4 use betweenness of points to write ac = ab + bc. 4x - 12 = x + 2x + 3. 4x - 12 = 3x + 3. x - 12 = 3. x = 15. now find bc. bc = 2x + 3 = 2(15) + 3 = 33.

Explanation:

Step1: Set up the equation using betweenness

Since $AC = AB+BC$, and $AB = x$, $BC = 2x + 3$, $AC=4x - 12$, we have $4x-12=x + 2x+3$.

Step2: Combine like - terms

Combining the $x$ terms on the right - hand side of the equation $4x-12=x + 2x+3$, we get $4x-12 = 3x+3$.

Step3: Isolate the variable $x$

Subtract $3x$ from both sides of the equation $4x-12 = 3x+3$. So, $(4x - 3x)-12=(3x-3x)+3$, which simplifies to $x-12 = 3$.

Step4: Solve for $x$

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

Step5: Find the value of $BC$

Substitute $x = 15$ into the formula for $BC$. Since $BC=2x + 3$, then $BC=2\times15+3=30 + 3=33$.

Answer:

$33$