Question 1

Solve the linear equation for $$x$$: $$5x - 3 = 2x + 9.$$

Accepted Answer

$$x = 4$$

Question 2

Which of the following is the correct solution set for the quadratic equation $$x^2 - 6x + 8 = 0$?

Accepted Answer

$$x = 2,\ x = 4$$

Question 3

Simplify the following expression involving complex numbers: $$(3 + 2i) + (4 - 5i).$$

Accepted Answer

$$7 - 3i$$

Question 4

Solve the radical equation for $$x$$: $$\sqrt{x + 5} = 4.$$

Accepted Answer

$$x = 11$$

Question 5

Which of the following is the solution to the inequality $$2x - 7 \u003e 3$$?

Accepted Answer

$$x \u003e 5$$

Question 6

Solve the absolute value equation: $$|3x - 2| = 7.$$

Accepted Answer

$$x = 3,\ x = -\dfrac{5}{3}$$

Question 7

A chemist needs to mix a $$20\%$$ saline solution with a $$50\%$$ saline solution to obtain $$10$$ liters of a $$30\%$$ solution. How many liters of the $$20\%$$ solution should be used?

Accepted Answer

$$6.67$$ liters

Question 8

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$15$$

Question 9

Which of the following is the conjugate of the complex number $$5 - 2i$$?

Accepted Answer

$$5 + 2i$$

Question 10

A bank offers an annual interest rate of $$6\%$$ compounded annually. If you invest $$\1000$, how much will you have after 3$ years? (Round to the nearest dollar.)

Accepted Answer

$$1191$$

Question 11

Solve for $$x$$: $$x^2 + 2x + 5 = 0$.

Accepted Answer

$$x = -1 \pm 2i$$

Question 12

Which of the following is the solution to the inequality $$|x - 4| \u003c 3$$?

Accepted Answer

$$1 \u003c x \u003c 7$$

Question 13

If $$x = 2 + 3i$$ and $$y = 1 - 2i$$, what is $$x \cdot y$$?

Accepted Answer

$$8 - i$$

Question 14

Solve the radical equation: $$\sqrt{2x + 1} = x.$$

Accepted Answer

$$x = 1$$

Question 15

A solution is made by mixing $$4$$ liters of a $$10\%$$ acid solution with $$x$$ liters of a $$30\%$$ acid solution to obtain a $$20\%$$ acid solution. What is the value of $$x$$?

Accepted Answer

$$4$$

Chapter 1: Equations and Inequalities – College Algebra Study Guide

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