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

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 ✎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*.If

*z*is more than one, thenis more than one. *y*= 38 if*y*= 5*x*^{3}− 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

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

*z* = 3 3 > 1

Write the hypothesis and conclusion.

Hypothesis: *y* = 5*x*^{3} − 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