Question 1

Solve the equation: $$3x + 7 - 6(x + 1) = 5x + 8$$

Accepted Answer

$$x = -1$$

Question 2

Which of the following is the correct solution set in interval notation for the inequality $$14 \leq 2y + 20 \leq 24$$?

Accepted Answer

$$[-3, 2]$$

Question 3

Perform the operation and simplify: $$(3 - 7i)(4 + i)$$

Accepted Answer

$$19 - 25i$$

Question 4

A chemist is mixing two solutions. The equation $$3x + 7 - 6(x + 1) = 5x + 8$$ models the number of grams of a substance in the mixture. What is the value of $$x$$ that balances the equation?

Accepted Answer

$$x = -1$$

Question 5

Which of the following represents the correct first step in solving $$3x + 7 - 6(x + 1) = 5x + 8$$?

Accepted Answer

$$3x + 7 - 6x - 6 = 5x + 8$$

Question 6

If $$2y + 20$$ represents the temperature in degrees Celsius, for which values of $$y is $$the temperature between $$14$$ and $$24$$ degrees inclusive?

Accepted Answer

$$y \in [-3, 2]$$

Question 7

Which of the following is the correct expanded form of $$(3 - 7i)(4 + i)$$?

Accepted Answer

$$12 + 3i - 28i - 7i^2$

Question 8

A medical researcher uses the inequality $$14 \leq 2y + 20 \leq 24 to $$represent a safe dosage range for a drug, where $$y is $$the number of pills. What is the maximum number of pills that can be safely administered?

Accepted Answer

$$2$$

Question 9

Which of the following is the correct simplification for $$-7i^2$$?

Accepted Answer

$$7$$

Question 10

If $$x$$ represents the number of years since a company was founded, and the equation $$3x + 7 - 6(x + 1) = 5x + 8$$ models its profit, in which year does the company break even?

Accepted Answer

$$x = -1$$

Question 11

Which of the following is the correct interval notation for all $$y$$ such that $$14 \leq 2y + 20 \leq 24$$?

Accepted Answer

$$[-3, 2]$$

Question 12

Which of the following is the correct result of multiplying $$(3 - 7i)(4 + i)$$?

Accepted Answer

$$19 - 25i$$

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