Question

question point b is on line segment ac. given ab = 4x - 6, ac = 2x + 10, and bc = 4, determine the numerical length of ac. answer attempt 2 out of 2 ac = 34 submit answer watch video show examples

Explanation:

Step1: Use segment - addition postulate

Since $AC=AB + BC$, we substitute the given expressions: $2x + 10=(4x - 6)+4$.

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: $(4x - 6)+4=4x-2$. So, $2x + 10=4x-2$.

Step3: Solve for x

Subtract $2x$ from both sides: $10 = 4x-2-2x$, which simplifies to $10 = 2x-2$. Then add 2 to both sides: $10 + 2=2x$, so $12 = 2x$. Divide both sides by 2: $x = 6$.

Step4: Find the length of AC

Substitute $x = 6$ into the expression for $AC$. Since $AC=2x + 10$, then $AC=2\times6+10=12 + 10=22$.

Answer:

22