Question 1

Solve for $$x$$: $$13x - 9 = 6(2x + 3) - 9. $$What is the value of $$x$$?

Accepted Answer

$$x = 2$$

Question 2

Which of the following is the solution to $$\dfrac{1}{2}(2x + 3) = \dfrac{1}{3}(x - 5)$$?

Accepted Answer

$$x = -3$$

Question 3

A chemist mixes two solutions, represented by $$6x + 4 - 9(x + 1) = 8x + 3. $$What is the value of $$x$$ after the reaction?

Accepted Answer

$$x = -1$$

Question 4

Solve for $$x$$: $$2(5 - 2x) - 3x = 15 + 3x. $$What is the value of $$x$$?

Accepted Answer

$$x = -2$$

Question 5

Simplify the expression: $$3x^2y^3$ + 12x^2$y^3$$ - $$30x^2y^3$

Accepted Answer

$$-15x^2y^3$

Question 6

A projectile's height is modeled by $$h = x^2$ + 13x - 48. $$What are the $$x-$$intercepts?

Accepted Answer

$$x = -16, x = 3$$

Question 7

Factor the quadratic: $$m^2 + 16m + 45$

Accepted Answer

$$(m + 5)(m + 9)$$

Question 8

Solve for $$x$$: $$14x^2 + 37x = 5$

Accepted Answer

$$x = \dfrac{-37 \pm \sqrt{37^2$ - 4 \cdot 14 \cdot (-5)}}{2 \cdot 14}$$

Question 9

A company’s profit is modeled by $$x^2 - 121$. What are the real solutions for x$?

Accepted Answer

$$x = 11, x = -11$$

Question 10

Solve the quadratic equation: $$x^2 - 17x + 72 = 0$

Accepted Answer

$$x = 8, x = 9$$

Question 11

Which of the following is the solution to $$x^2 - 10x + 15 = 0$?

Accepted Answer

$$x = 5 \pm \sqrt{15}$$

Question 12

Solve for $$x$$: $$-9x^2 - 8x + 7 = 0$

Accepted Answer

$$x = \dfrac{-8 \pm \sqrt{64 - 4 \cdot (-9) \cdot 7}}{2 \cdot (-9)}$$

Question 13

Which of the following is the solution set for $$x^2 = 25$?

Accepted Answer

$$(-5, 5)$$

Question 14

Calculate $$i^3$$ where $$i is $$the imaginary unit.

Accepted Answer

$$-i$$

Question 15

Simplify $$\sqrt{-3} \cdot \sqrt{-75}$$ using properties of complex numbers.

Accepted Answer

$$15i$$

Question 16

Simplify $$-15\sqrt{-27}$$ using properties of complex numbers.

Accepted Answer

$$-5i\sqrt{3}$$

Question 17

Simplify $$(4 - 3i)^2$.

Accepted Answer

$$7 - 24i$$

Question 18

A medical imaging device uses the complex number $$8 + 7i to $$represent a signal. If the signal is doubled, what is the new value?

Accepted Answer

$$16 + 14i$$

Question 19

Simplify $$\dfrac{3 + 5i}{5 - 6i}$$ and write in the form $$a + bi.$$

Accepted Answer

$$\dfrac{30 + 29i}{11}$$

College Algebra Study Guide: Linear Equations, Quadratic Equations, and Complex Numbers

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