Q: A chemist needs to prepare a solution by mixing two chemicals. The equation $$x + 5x + 6 = 0$$ models the total amount needed. What are the possible values for $$x$$?

$$x = -2$$ \, \text{or} \, x = -3$

Question 1

Which of the following is the correct solution to the equation $$3(x-2) = 15$$?

Accepted Answer

$$x = 7$$

Question 2

A chemist needs to prepare a solution by mixing two chemicals. The equation $$x + 5x + 6 = 0$$ models the total amount needed. What are the possible values for $$x$$?

Accepted Answer

$$x = -2$$ \, 	ext{or} \, x = -3$

Question 3

Simplify the expression $$4(2x-3) - (x+5).$$

Accepted Answer

$$7x - 17$$

Question 4

A medical researcher models the growth of bacteria with the equation $$2x = 10. $$What is the value of $$x$$?

Accepted Answer

$$x = 5$$

Question 5

Solve for $$x in $$the equation $$x + 1 = 3(x - 2)$$, which models the number of hours a student needs to study to pass an exam.

Accepted Answer

$$x = 5$$

Question 6

Which of the following is the correct factorization for the quadratic equation $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$(x-2)(x-3) = 0$$

Question 7

A business owner wants to solve $$3x = 9 to $$determine the number of products to sell. What is the solution?

Accepted Answer

$$x = 3$$

Question 8

If $$4x - 7 = 9$$, what is the value of $$x$$?

Accepted Answer

$$x = 4$$

Question 9

A student is given the equation $$2x + 4 = 10 to $$solve for $$x. $$What is the correct solution?

Accepted Answer

$$x = 3$$

Question 10

Which of the following expressions is equivalent to $$8x - (2x + 5)$$?

Accepted Answer

$$6x - 5$$

Question 11

A biologist uses the equation $$x + 1 = 3(x - 2) to $$model population growth. What is the correct step to isolate $$x$$?

Accepted Answer

$$x + 1 = 3x - 6$$

Question 12

If $$x = 2 or$$ $$x = 3$$ are solutions to a quadratic equation, which equation could it be?

Accepted Answer

$$x^2 - 5x + 6 = 0$

Question 13

A student simplifies $$4(2x-3) - (x+5). $$What is the first step?

Accepted Answer

$$8x - 12 - x - 5$$

Question 14

Solve for $$x in $$the equation $$5x = 20.$$

Accepted Answer

$$x = 4$$

Question 15

A student is asked to solve $$x + 1 = 3(x - 2). $$What is the value of $$x$$ after simplifying?

Accepted Answer

$$x = 5$$

Question 16

Which of the following is the correct solution to $$2x = 10$$?

Accepted Answer

$$x = 5$$

Question 17

A student is given the equation $$3(x-2) = 15. $$What is the correct first step to solve for $$x$$?

Accepted Answer

$$x - 2 = 5$$

Question 18

If $$x = 2 or$$ $$x = 3$$ are solutions to a quadratic equation, what is the sum of the roots?

Accepted Answer

$$5$$

Question 19

A student is asked to solve $$x + 1 = 3(x - 2). $$What is the correct equation after expanding the right side?

Accepted Answer

$$x + 1 = 3x - 6$$

Question 20

A student is given the equation $$x^2 - 5x + 6 = 0$. What is the product of the roots?

Accepted Answer

$$6$$

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