The projectile never reaches the ground (no real solution).

Question 1

Solve for $x$: $9x - 5 = 7 + 4x$.

Accepted Answer

$x = \dfrac{12}{5}$

Question 2

Which of the following is the solution to $3(7x - 5) - (6x - 9) = 5x + 12$?

Accepted Answer

$x = \dfrac{19}{10}$

Question 3

Simplify the expression $(6 + 5i) - (8 - 6i)$, where $i$ is the imaginary unit.

Accepted Answer

$-2 + 11i$

Question 4

Solve for $x$ using the square root property: $6x^2 = 150$.

Question 5

Solve the quadratic equation $x^2 + 7x + 4 = 0$ by completing the square.

Accepted Answer

$x = -\dfrac{7}{2} \pm \dfrac{\sqrt{33}}{2}$

Question 6

Which of the following is the solution to $x^2 + 2x + 26 = 0$ using the quadratic formula?

Accepted Answer

$x = -1 \pm 5i$

Question 7

Solve the inequality $6x - 5 \leq 8$ and express the solution in interval notation.

Accepted Answer

$(-\infty, \dfrac{13}{6}]$

Question 8

Given the equation $\sqrt{8} (\sqrt{3} - \sqrt{7})$, simplify the expression.

Accepted Answer

$2\sqrt{6} - 2\sqrt{14}$

Question 9

Solve for $x$: $(x - 2)^2 = 96$.

Accepted Answer

$x = 2 \pm 4\sqrt{6}$

Question 10

Solve the equation $4x - 3x^2 = 0$.

Accepted Answer

$x = 0$ or $x = 1$

Question 11

Which of the following is the solution to $6x^2 = 150$?

Question 12

Solve the inequality $-55 < 3x + 13 \leq 34$ and express the solution in interval notation.

Accepted Answer

$(-6, 7]$

Question 13

Simplify $(-4 + 8i) + (4 + 8i)$.

Accepted Answer

$0 + 16i$

Question 14

Solve for $x$: $x^2 + 7x + 4 = 0$ using the quadratic formula.

Accepted Answer

$x = -\dfrac{7}{2} \pm \dfrac{\sqrt{33}}{2}$

Question 15

Given $x^2 + 2x + 26 = 0$, what are the solutions?

Accepted Answer

$x = -1 \pm 5i$

Question 16

Solve the inequality $72 + 4x < 18$ and express the solution in interval notation.

Accepted Answer

$(-\infty, -14)$

Question 17

If $x^2 + 2x + 26 = 0$ models the height of a projectile in meters, what does the solution $x = -1 \pm 5i$ indicate about the projectile?

Accepted Answer

The projectile never reaches the ground (no real solution).

Question 18

Solve for $x$: $6x - 5 \leq 8$.

Accepted Answer

$x \leq \dfrac{13}{6}$

Question 19

Which of the following is the solution to $x^2 + 2x + 26 = 0$ using the quadratic formula?

Accepted Answer

$x = -1 \pm 5i$

College Algebra: Solving Equations, Simplifying Expressions, and Solving Inequalities

Study Guide - Practice Questions