Question

given the line segment ac with point b as the midpoint of segment ac, answer the following questions. ab = 3(x + 10) and bc = 2(5 + 4x) find x x = blank find ab ab = blank find ac ac = blank

Explanation:

Step1: Set AB equal to BC

Since B is mid - point of AC, AB = BC. So, $3(x + 10)=2(5 + 4x)$.

Step2: Expand both sides

Expand the left - hand side: $3x+30$, and the right - hand side: $10 + 8x$. So the equation becomes $3x+30=10 + 8x$.

Step3: Solve for x

Subtract 3x from both sides: $30=10 + 5x$. Then subtract 10 from both sides: $20 = 5x$. Divide both sides by 5, we get $x = 4$.

Step4: Find AB

Substitute x = 4 into the expression for AB. AB=$3(x + 10)=3(4 + 10)=3\times14 = 42$.

Step5: Find AC

Since AC = AB+BC and AB = BC, AC = 2AB. So AC = 2×42 = 84.

Answer:

x = 4
AB = 42
AC = 84