Question 1

Solve the inequality $$3x + 2 \u003c 7$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, \frac{5}{3})$$

Question 2

Which of the following represents the solution to $$2x - 5 \geq 3 in $$interval notation?

Accepted Answer

$$[4, \infty)$$

Question 3

Given the quadratic equation $$x^2 - 5x + 6 = 0$, what are the solutions?

Accepted Answer

$$x = 2$$ and $$x = 3$$

Question 4

Solve the rational equation $$\frac{2x}{x-1} = 4$$ for $$x.$$

Accepted Answer

Question 5

Which of the following is the correct interval notation for all real numbers $$x$$ such that $$a \u003c x \u003c b$$?

Accepted Answer

$$(a, b)$$

Question 6

If $$x^2 - 4$$ \u003c 0$$, what is the solution in interval notation?

Accepted Answer

$$(-2, 2)$$

Question 7

Solve the equation $$\sqrt{x+3} = 5.$$

Accepted Answer

$$x = 22$$

Question 8

Which of the following is the factored form of $$x^2 - 9$?

Accepted Answer

$$(x + 3)(x - 3)$$

Question 9

Given the grouping $$x^2 + 5x + 6$, which of the following is a correct factorization?

Accepted Answer

$$(x + 2)(x + 3)$$

Question 10

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in hundreds). For what values of $$x is $$the profit at least zero?

Accepted Answer

Question 11

Solve the inequality $$x^2 - 4x + 3$$ \u003e 0$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 1) \cup (3, \infty)$$

Question 12

Which of the following is the solution to $$|2x - 3| = 7$$?

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 13

If $$x^2 + 2x - 8 = 0$, what are the solutions for x$?

Accepted Answer

$$x = 2 or$$ $$x = -4$$

Question 14

Which of the following is the correct solution to $$\frac{3x}{x+2} = 6$$?

Accepted Answer

$$x = 2$$

Question 15

Solve the radical equation $$\sqrt{2x + 3} = 5.$$

Accepted Answer

$$x = 11$$

Question 16

Which of the following is the correct factorization for $$x^2 + 6x + 9$?

Accepted Answer

$$(x + 3)^2$

Question 17

If $$x^2 - 16$$ \leq 0$$, what is the solution in interval notation?

Accepted Answer

$$[-4, 4]$$

Question 18

Which of the following is the solution to $$x^2 = 9$?

Accepted Answer

$$x = 3 or$$ $$x = -3$$

Question 19

A ball is thrown upward and its height $$h (in $$meters) after $$t$$ seconds is given by $$h = -5t^2$ + 20t + 1. $$For what values of $$t is $$the ball at least 16 meters above the ground?

Accepted Answer

$$t \in [0.5, 3.5]$$

Equations and Inequalities: Precalculus Study Notes

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