Heidi solved the equation 3(x + 4) + 2 = 2 + 5(x – 4). Her steps are below:

3x + 12 + 2 = 2 + 5x – 20
3x + 14 = 5x – 18
14 = 2x – 18
32 = 2x
16 = x
Use the drops-downs to justify how Heidi arrived at each step.

ANSWERS:
Step 1:
✔ distributive property

Step 2:
✔ combine like terms

Step 3:
✔ subtraction property of equality

Step 4:
✔ addition property of equality

Step 5:
✔ division property of equality

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e.g. 98.76543).