Question

b. 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 postulate

Since $AB=x + 18$, $BC = 3x+25$ and $AC=19$, by the Segment Addition Postulate $AB + BC=AC$, 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 of the equation: $(x+3x)+(18 + 25)=19$, which simplifies to $4x+43 = 19$.

Step3: Isolate the variable term

Use the Subtraction Property of Equality (P.O.E.). Subtract 43 from both sides of the equation $4x+43 = 19$. We have $4x+43-43=19 - 43$, which 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:

$x=-6$