Question 1

Which of the following equations represents a line that passes through the point $$(2, -3)$$ and has a slope of $$4$$?

Accepted Answer

$$y = 4x - 11$$

Question 2

A chemist is mixing two solutions: one with $$30\%$$ acid and another with $$50\%$$ acid. How many liters of each should be mixed to obtain $$10$$ liters of a $$42\%$$ acid solution?

Accepted Answer

$$4$$ liters of $$30\%$$ and $$6$$ liters of $$50\%$$

Question 3

Which of the following is the solution set for the inequality $$2x - 5 \u003c 3x + 1$$?

Accepted Answer

$$x \u003e -6$$

Question 4

A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. If a customer paid $$\61$ in total, how many miles did they drive?

Accepted Answer

$$180$$ miles

Question 5

Which of the following is the correct solution to the system of equations:

$$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2,\ y = 1$$

Question 6

Which of the following is the equation of a line perpendicular to $$y = -\frac{1}{2}x + 4$$ and passing through the point $$(4, 1)$$?

Accepted Answer

$$y = 2x - 7$$

Question 7

A biologist is studying the population of a bacteria culture, which doubles every $$3$$ hours. If the initial population is $$500$$, what will the population be after $$9$$ hours?

Accepted Answer

$$4000$$

Question 8

Solve for $$x$$: $$|3x - 7| = 8$$

Accepted Answer

$$x = 5,\ x = -\frac{1}{3}$$

Question 9

Which of the following represents the solution to the compound inequality $$-2 \u003c 3x + 1 \leq 7$$?

Accepted Answer

$$-1 \u003c x \leq 2$$

Question 10

A business's profit $$P (in $$dollars) is given by $$P = 50x - 1200$$, where $$x is $$the number of units sold. How many units must be sold for the business to break even?

Accepted Answer

$$24$$

Question 11

Which of the following is the solution to the system of equations:

$$\begin{cases} x + 2y = 8 \ 3x - y = 5 \end{cases}$$

Accepted Answer

$$x = 3,\ y = 2.5$$

Question 12

A medication is administered at a rate that decreases by $$10\%$$ each hour. If the initial dose is $$200 mg$$, how much remains after $$3$$ hours?

Accepted Answer

$$145.8 mg$$

Question 13

Which of the following is the solution set for $$2(x - 3) \geq 4x + 1$$?

Accepted Answer

$$x \leq -3$$

Question 14

A cell phone plan charges $$\40$ per month plus $$\$$0.10$$ per text message. If a customer's bill was $$\55$, how many text messages did they send?

Accepted Answer

$$150$$

Question 15

Which of the following is the equation of a line parallel to $$y = 3x - 2$$ and passing through the point $$(1, 4)$$?

Accepted Answer

$$y = 3x + 1$$

Question 16

Solve for $$x$$: $$5x + 2 = 3x - 6$$

Accepted Answer

$$x = -4$$

Question 17

A mixture contains $$8$$ pounds of nuts worth $$\6$ per pound and some nuts worth $$\$$10$$ per pound. If the mixture is to be worth $$\8$ per pound, how many pounds of $$\$$10$$ nuts should be added?

Accepted Answer

$$4$$ pounds

Question 18

Which of the following is the solution to the absolute value inequality $$|2x + 1| \leq 5$$?

Accepted Answer

$$-3 \leq x \leq 2$$

Question 19

A company produces widgets at a cost of $$C = 5x + 200$$, where $$x is $$the number of widgets. If the company sells each widget for $$\15$, how many widgets must be sold to break even?

Accepted Answer

$$20$$

Question 20

Which of the following is the solution to the system of equations:

$$\begin{cases} 4x - y = 9 \ 2x + 3y = 1 \end{cases}$$

Accepted Answer

$$x = 2,\ y = -1$$

Chapter 2 Review: Equations & Inequalities – Study Notes

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