Question 1

Solve the linear equation for $$x$$: $$3x - 7 = 17$$

Accepted Answer

$$x = 8$$

Question 2

A rational expression is given by $$\dfrac{6}{x-9}. $$What is the restriction on $$x$$?

Accepted Answer

$$x 
eq 9$$

Question 3

After a 70% reduction, you purchase a new table for $150. What was the original price of the table?

Accepted Answer

$$500$$

Question 4

Including a 7% sales tax, a watch sells for $2,024.24. What was the price of the watch before tax?

Accepted Answer

$$1,892.00$$

Question 5

You invested $$30,000 in two accounts paying 6% and 7% annual interest, respectively. If the total interest earned for the year was 2$$,000, how much was invested at 6%?

Accepted Answer

Question 6

Perform the addition and express in standard form: $$(4 + 3i) + (6 - i)$$

Accepted Answer

$$10 + 2i$$

Question 7

Perform the multiplication and express in standard form: $$(-5 + 4i)(3 + i)$$

Accepted Answer

$$-19 + 7i$$

Question 8

Find the conjugate of the complex number $$6 + 7i.$$

Accepted Answer

$$6 - 7i$$

Question 9

Simplify: $$\sqrt{-64}$$

Accepted Answer

$$8i$$

Question 10

Solve by factoring: $$3x^2 + 12x = 0$

Accepted Answer

$$x = 0, x = -4$$

Question 11

Solve using the quadratic formula: $$x^2 - 6x + 10 = 0$

Accepted Answer

$$x = 3 \pm i$$

Question 12

Solve the radical equation: $$\sqrt{x + 3} + 3 = x$$

Accepted Answer

$$x = 4$$

Question 13

Solve and check the absolute value equation: $$|x - 2| = 7$$

Accepted Answer

$$x = 9 or$$ $$x = -5$$

Question 14

Solve the linear equation using the zero product principle: $$x^2 - 5x = -6$

Accepted Answer

$$x = 2, x = 3$$

Question 15

Simplify: $$\sqrt{-27} + \sqrt{-48}$$

Accepted Answer

$$3i\sqrt{3} + 4i\sqrt{3} = 7i\sqrt{3}$$

Question 16

Solve by using the square root property: $$(x - 5)^2$ = 9$$

Accepted Answer

$$x = 8 or$$ $$x = 2$$

Question 17

Solve the equation by any method: $$5x^2 - 10 = 0$

Accepted Answer

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

Question 18

Solve and check the equation: $$\left( x - 4 \$$right)^{2/3}$$ = 16$$

Accepted Answer

$$x = 20 or$$ $$x = -12$$

Question 19

Perform the division and express in standard form: $$\dfrac{2 + 3i}{2 - i}$$

Accepted Answer

$$\dfrac{1}{5} + \dfrac{8}{5}i$$

Question 20

Solve the radical equation: $$\sqrt{2x + 13} = x + 7$$

Accepted Answer

$$x = 2$$

College Algebra Exam 1 Study Guide – Step-by-Step Guidance

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