Q: A chemist needs to mix a 10% saline solution with a 30% saline solution to obtain 20 liters of a 25% saline solution. Let $$x be $$the amount (in liters) of the 10% solution used. Which equation models this scenario?

$$0.10x + 0.30(20 - x) = 0.25 \times 20$$

Question 1

Which of the following equations represents a linear equation in one variable?

Accepted Answer

$$2x + 5 = 11$$

Question 2

Solve for $$x$$: $$3(x - 2) = 2x + 4$$

Accepted Answer

Question 3

Which of the following is the correct solution to the equation $$5x - 7 = 3x + 9$$?

Accepted Answer

$$x = 8$$

Question 4

A chemist needs to mix a 10% saline solution with a 30% saline solution to obtain 20 liters of a 25% saline solution. Let $$x be $$the amount (in liters) of the 10% solution used. Which equation models this scenario?

Accepted Answer

$$0.10x + 0.30(20 - x) = 0.25 	imes 20$$

Question 5

Which of the following is the solution set for the inequality $$2x - 5 \u003c 9$$?

Accepted Answer

$$x \u003c 7$$

Question 6

If $$f(x) = 3x - 4$$, what is $$f(2)$$?

Accepted Answer

$$2$$

Question 7

Which of the following best describes the graph of $$y = -2x + 5$$?

Accepted Answer

A straight line with a negative slope

Question 8

Solve the proportion: $$\frac{3}{x} = \frac{6}{8}$$

Accepted Answer

$$x = 4$$

Question 9

Which of the following is the solution to the equation $$\frac{2x}{5} = 8$$?

Accepted Answer

$$x = 20$$

Question 10

A car rental company charges a flat fee of $$\50$ plus $$\$$0.20$$ per mile driven. Which equation represents the total cost $$C$$ for driving $$m$$ miles?

Accepted Answer

$$C = 50 + 0.20m$$

Question 11

Which of the following is the solution to the equation $$|x - 3| = 7$$?

Accepted Answer

$$x = 10 or$$ $$x = -4$$

Question 12

Which of the following is the correct solution to the compound inequality $$-2 \u003c x + 1 \leq 5$$?

Accepted Answer

$$-3 \u003c x \leq 4$$

Question 13

A rectangle has a length that is 3 times its width. If the perimeter is 48 units, what is the width?

Accepted Answer

$$6$$

Question 14

Which of the following is the solution to the equation $$2(x - 3) = 4x + 6$$?

Accepted Answer

$$x = -6$$

Question 15

If $$y$$ varies directly as $$x$$ and $$y = 12$$ when $$x = 4$$, what is the value of $$y$$ when $$x = 10$$?

Accepted Answer

$$y = 30$$

Question 16

Which of the following is the solution to the equation $$\frac{x}{3} + 2 = 5$$?

Accepted Answer

$$x = 9$$

Question 17

A student scored 85, 90, and 95 on three tests. What score must the student get on the fourth test to have an average of 90?

Accepted Answer

$$90$$

Question 18

Which of the following is the solution to the equation $$4x + 7 = 3x - 2$$?

Accepted Answer

$$x = -9$$

Question 19

If $$a = 2$$ and $$b = -3$$, what is the value of $$2a - 3b$$?

Accepted Answer

$$13$$

Question 20

Which of the following is the solution to the equation $$\frac{5}{x} = 2$$?

Accepted Answer

$$x = 2.5$$

Unit 2 Review: Linear Equations, Ratios, and Proportions

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