Question 1

Which of the following is the correct definition of a linear equation in one variable?

Accepted Answer

$$ax + b = 0$$, where $$a$$ and $$b$$ are real numbers and $$a 
eq 0$$

Question 2

Solve the equation $$4(2x + 1) = 29 + 3(2x - 5)$$ for $$x.$$

Accepted Answer

$$x = 5$$

Question 3

Which operation does NOT generate an equivalent equation?

Accepted Answer

Multiplying both sides by zero

Question 4

Solve the equation $$\frac{x-3}{4} = \frac{5}{14} - \frac{x+5}{7}.$$

Accepted Answer

$$x = 1$$

Question 5

A rational equation is given by $$\frac{6}{x+3} - \frac{5}{x-2} = \frac{-20}{x^2$ + x - 6}. $$What is the solution set?

Accepted Answer

$$\{7\}$$

Question 6

Solve for $$q in $$the formula $$\frac{1}{p} + \frac{1}{q} = \frac{1}{f}.$$

Accepted Answer

$$q = \frac{pf}{p-f}$$

Question 7

Which statement about absolute value equations is correct?

Accepted Answer

If $$|u| = c$$ and $$c \u003c 0$$, there is no solution.

Question 8

Solve the absolute value equation $$|-2x| = 6.$$

Accepted Answer

Question 9

Which of the following is the standard form of a quadratic equation?

Accepted Answer

$$ax^2 + bx + c = 0$

Question 10

Solve the quadratic equation $$2x^2 - x = 0$ by factoring.

Accepted Answer

$$x = 0 or$$ $$x = \frac{1}{2}$$

Question 11

Which principle allows us to set each factor equal to zero when solving $$(x-3)(x+2)=0$$?

Accepted Answer

Zero-Product Principle

Question 12

Solve $$x^2 + 4x = 1$ by completing the square.

Accepted Answer

$$x = -2 \pm \sqrt{5}$$

Question 13

Which formula is used to solve any quadratic equation $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 14

Given the quadratic equation $$3x^2 - 2x + 5 = 0$, what does the discriminant tell you about the solutions?

Accepted Answer

There are two imaginary solutions.

Question 15

Which is the most efficient method to solve $$x^2 - 6x = -7$?

Accepted Answer

Completing the square

Question 16

Solve the radical equation $$\sqrt{x} = 6.$$

Accepted Answer

$$x = 36$$

Question 17

A medical test uses the formula $$C = 2\sqrt{t} to $$estimate the concentration $$C of a $$drug in the bloodstream $$t$$ hours after administration. If $$C = 10$$, how many hours after administration is the concentration measured?

Accepted Answer

$$t = 25$$

Question 18

If the discriminant $$b^2 - 4ac$ of a quadratic equation is zero, what can you conclude about the solutions?

Accepted Answer

There is one real (repeated) solution.

Question 19

Solve the equation $$|3x - 2| = 7.$$

Accepted Answer

$$x = 3 or$$ $$x = -\frac{5}{3}$$

Chapter P: Prerequisites – Fundamental Concepts of Algebra (P.7 Equations)

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