Question

tulate- if 3 points are collinear____ d b is between a and c, then ab + bc = ac

1. if mo = 32, find the value of x.

mn+no = mo
2x + 3x+7 = 32
5x+7 = 32

1. solve for x. then find the length of each segment.

statements reasons
jk = mn
jk + kl = jl
mn+kl = jl

Explanation:

Step1: Set up equation using segment - addition postulate

Since the sum of the lengths of smaller segments equals the length of the larger segment, we have $x+(x + 15)+3x=10x + 5$.

Step2: Combine like - terms on the left - hand side

Combining the $x$ terms on the left side gives $(1 + 1+3)x+15=5x + 15$. So, $5x+15=10x + 5$.

Step3: Isolate the variable terms

Subtract $5x$ from both sides: $5x+15-5x=10x + 5-5x$, which simplifies to $15 = 5x+5$.

Step4: Solve for $x$

Subtract 5 from both sides: $15 - 5=5x+5 - 5$, getting $10 = 5x$. Then divide both sides by 5: $\frac{10}{5}=\frac{5x}{5}$, so $x = 2$.

Step5: Find the length of each segment

• The first segment has length $x=2$.
• The second segment has length $x + 15=2 + 15=17$.
• The third segment has length $3x=3\times2 = 6$.
• The fourth segment has length $10x + 5=10\times2+5=20 + 5=25$.

Answer:

$x = 2$; lengths of segments are 2, 17, 6, 25.