Question 1

Solve the equation $9x + 11 = 7x + 1$. What is the value of $x$?

Accepted Answer

$x = 5$

Question 2

Simplify $\sqrt{-90}$ and write your answer in standard form.

Accepted Answer

$3\sqrt{10}i$

Question 3

Which of the following is the result of $(5 - i)(3 + 4i)$?

Accepted Answer

$19 + 17i$

Question 4

Solve the quadratic equation $x^2 + 2x - 35 = 0$ by factoring.

Accepted Answer

$x = 5$ or $x = -7$

Question 5

A square flower bed is enlarged by adding 2 meters to each side. If the area of the larger square is 196 square meters, what is the length of a side of the original square?

Accepted Answer

$12$ meters

Question 6

Jill can paint a fence in 18 hours, and her sister Jan can do it in 12 hours. How long will it take them to paint the fence together?

Accepted Answer

$7\dfrac{1}{5}$ hours

Question 7

Solve the inequality $-5x - 4 \geq 3(2x - 5)$. Express your answer in interval notation.

Accepted Answer

$(-\infty, 1]$

Question 8

The cost to produce $x$ units of earbuds is $C = 3x + 1500$ and the revenue is $R = 8x$. For what values of $x$ will the company at least break even?

Accepted Answer

$[300, \infty)$

Question 9

Solve the equation $|4x + 7| = 0$.

Accepted Answer

$x = -\dfrac{7}{4}$

Question 10

A projectile is launched upward from the ground. Its height in feet after $t$ seconds is $s = -16t^2 + 320t$. After how many seconds will it hit the ground?

Accepted Answer

$20$ seconds

Question 11

Solve the equation $x^2 + 10 = 0$ using the square root property.

Accepted Answer

$x = \pm \sqrt{10}i$

Question 12

Solve the quadratic equation $8x^2 - 4x + 1 = 0$ by completing the square.

Accepted Answer

$x = \dfrac{1}{4} \pm \dfrac{i}{4}$

Question 13

Solve the equation $\dfrac{3}{4}x + \dfrac{5}{5} = \dfrac{5}{5}x - \dfrac{2}{5}$.

Accepted Answer

$x = 6$

Question 14

The length of a rectangle is 4 meters longer than its width. If the area is 8 square meters, what are the rectangle's dimensions (rounded to the nearest tenth)?

Accepted Answer

$1.5$ meters by $5.5$ meters

Question 15

Solve the inequality $|2x + 9| \leq 3$. Express your answer in interval notation.

Accepted Answer

$[-6, -3]$

Question 16

Which of the following is the simplified form of $(4 - 3i)^2$?

Accepted Answer

$7 - 24i$

Question 17

Solve the quadratic equation $2x^2 + 10x = 0$ by factoring.

Accepted Answer

$x = 0$ or $x = -5$

Question 18

Solve the equation $|5x - 1| = 2x + 3$.

Accepted Answer

$x = -2$ or $x = \dfrac{4}{7}$

Question 19

The longer leg of a right triangle exceeds the shorter leg by 1 inch, and the hypotenuse exceeds the longer leg by 7 inches. What are the lengths of the legs (rounded to the nearest tenth)?

Accepted Answer

$17.6$ inches and $18.6$ inches

Question 20

Solve the inequality $x^2 + 3x - 4 \leq 0$ and express your answer in interval notation.

Accepted Answer

$[-4, 1]$

College Algebra Exam Review: Step-by-Step Guidance

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