  ### Home > CAAC > Chapter 6 > Lesson 6.2.5 > Problem6-86

6-86.
1. Identify the hypothesis and conclusion for each of the following statements. Then decide if the statement is sometimes true, always true, or never true. Justify your decision. You may want to review the meanings of hypothesis and conclusion from problem 6‑31. Homework Help ✎

1. If line l is parallel to line m and line m is parallel to line n,then line l must be parallel to line n.

2. If z is more than one, then is more than one.

3. y = 38 if y = 5x3 − 2 and x = 2.  Write the hypothesis and conclusion.

Hypothesis: line l is parallel to line m and that line m is parallel to line n.
Conclusion:line l must be parallel to line n.

Draw lines l, m, and n, so line l is parallel to line n and line m is parallel to line n.
Is there more than one way to draw this situation? Sometimes true, because line l and line n could coincide (overlap each other). Write the hypothesis and conclusion.

Hypothesis: z is more than one

$\text{Conclusion: }\frac{1}{z} \text{ is more than one.}$

Try an example, using a value greater than 1 for z.

z = 3 3 > 1

$\frac{1}{z}=\frac{1}{3} \text{ is } \frac{1}{3} >\text{ or }<1\text{?}\frac{1}{3}<1$

$\text{never true because }\frac{1}{x}<1\text{ if }x>1$ Write the hypothesis and conclusion.

Hypothesis: y = 5x3 − 2 and x = 2
Conclusion: y = 38

Substitute x = 2 into the equation and solve for y.
Find y:
y = 5(2)3 − 2
y = 5(8) − 2
y = 40 − 2
y = 38

Always true