Question

given: ac = 19
prove: x = -6
statements reasons
given
ab = x + 18
bc = 3x + 25
ab + bc = ac segment addition postulate
x + 18 + 3x + 25 = 19
4x + 43 = 19
subtraction p.o.e.
x = -6

Explanation:

Step1: Apply segment - addition

Since $AB + BC=AC$ (Segment Addition Postulate), and $AB=x + 18$, $BC = 3x+25$, $AC = 19$, we get the equation $x + 18+3x + 25=19$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms on the left - hand side: $(x+3x)+(18 + 25)=19$, which simplifies to $4x+43 = 19$.

Step3: Subtract 43 from both sides

Using the Subtraction Property of Equality (P.O.E.), we have $4x+43-43=19 - 43$. This gives $4x=-24$.

Step4: Solve for x

Divide both sides of the equation $4x=-24$ by 4. So, $\frac{4x}{4}=\frac{-24}{4}$, and $x=-6$.

Answer:

$x=-6$