Unit 7 Sample Work

Question

Solve the given equation. Remember to check for extraneous solutions. 3-2x=1-3x

1- Identify & Think : Do you understand what is being asked and what you need to do? Do you have a list of thing you know, ideas to try, and a plan for doing it? Identify the problem and list your strategies.

2-Do & Answer: Show your work to solve this problem. Check your work. Does your answer make sense? Show your work and report your answer clearly

Problem 2- -6log3(x-3)=-24

1- Identify & Think : Do you understand what is being asked and what you need to do? Do you have a list of things you know, ideas to try, and a plan for doing it? Identify the problem and list your strategies.

2-Do & Answer: Show your work to solve this problem. Check your work. Does your answer make sense? Show your work and report your answer clearly

Problem 3- 3/x+7+4/x-8

1- Identify & Think : Do you understand what is being asked and what you need to do? Do you have a list of things you know, ideas to try, and a plan for doing it? Identify the problem and list your strategies.

2-Do & Answer: Show your work to solve this problem. Check your work. Does your answer make sense? Show your work and report your answer clearly

Problem 4- -4,12,-36,108,-324,...

For the following sequence, state if it is arithmetic, geometric or neither. Justify your answer.

1-Identify & Think : Do you understand what is being asked and what you need to do? Do you have a list of things you know, ideas to try, and a plan for doing it? Identify the problem and list your strategies

2-Do & Answer: Show your work to solve this problem. Check your work. Does your answer make sense? Show your work and report your answer clearly.

Problem 5- 4p2 Evaluate

1-Identify & Think : Do you understand what is being asked and what you need to do? Do you have a list of things you know, ideas to try, and a plan for doing it? Identify the problem and list your strategies.

2- Do & Answer: Show your work to solve this problem. Check your work. Does your answer make sense? Show your work and report your answer clearly.

Answer 1

log_bx=a equivalent to b^a=x

example: log₂(16)=x --> 2^x= 16, x=4

Problem 1: (-6)log₃(x-3)=-24

divide both sides by (-6) gives log₃(x-3) = (-24/-6) = 4

this is equivalent to 3⁴=(x-3)

add 3 to both sides

3⁴ + 3 = x = 81+3=84

(problem 2 next)

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Problem 2

3-(3/x)+7+(4/x)-8 -----> assuming typo supposed to be =8

3-(3/x)+7+(4/x) = 8

collect like terms (not necessary but for organization / illustration)

3+7 -(3/x)+(4/x)=8

or

10 -(3/x)+(4/x)=8

subtract 10 from both sides

(-3/x)+(4/x) = -2 = (4/x) - (3/x) = (4-3)/x = 1/x

-2 = 1/x

multiply both sides by x, divide both sides by -2

-2x = 1

x = -1/2