Question

standard: g.gsr 4.1-dok2
point b lies on segment ac. ab = x + 1, ac = 3x + 12, and bc = 7x - 11.
what is the value of x?
2
4.4
5.75
8

Explanation:

Step1: Use segment - addition postulate

Since point B lies on segment AC, we have $AB + BC=AC$. Substituting the given expressions, we get $(x + 1)+(7x-11)=3x + 12$.

Step2: Simplify the left - hand side

Combine like terms: $x+7x + 1-11=8x-10$. So, the equation becomes $8x-10 = 3x+12$.

Step3: Isolate the variable x

Subtract $3x$ from both sides: $8x-3x-10=3x-3x + 12$, which simplifies to $5x-10 = 12$. Then add 10 to both sides: $5x-10 + 10=12 + 10$, giving $5x=22$.

Step4: Solve for x

Divide both sides by 5: $x=\frac{22}{5}=4.4$.

Answer:

$4.4$