Chapter 2

When solving an inequality, explain what happened from Step 1 to Step 2: Step \(1 -2 x >6\) Step 2 \( x < -3\)

In a radical equation, what does it mean if a number is an extraneous solution?

How do we recognize when an equation is quadratic?

Explain how to add complex numbers.

To set up a model linear equation to fit real-world applications, what should always be the first step?

What does it mean when we say that two lines are parallel?

Is it possible for a point plotted in the Cartesian coordinate system to not lie in one of the four quadrants? Explain.

When solving an inequality, we arrive at: $$\begin{array}{c} x+2

Explain why possible solutions must be checked in radical equations.

When we solve a quadratic equation, how many solutions should we always start out seeking? Explain why when solving a quadratic equation in the form \(a x^{2}+b x+c=0\) we may graph the equation \(y=a x^{2}+b x+c\) and have no zeroes ( \(x\) -intercepts).

What is the basic principle in multiplication of complex numbers?

Use your own words to describe this equation where \(n\) is a number: \(5(n+3)=2 n\).

What is the relationship between the slopes of perpendicular lines (assuming neither is horizontal nor vertical)?

Describe the process for finding the \(x\) -intercept and the \(y\) -intercept of a graph algebraically.

When writing our solution in interval notation, how do we represent all the real numbers?

Your friend tries to calculate the value \(-9^{\frac{3}{2}}\) and keeps getting an ERROR message. What mistake is he or she probably making?

When we solve a quadratic equation by factoring, why do we move all terms to one side, having zero on the other side?

Give an example to show that the product of two imaginary numbers is not always imaginary.

If the total amount of money you had to invest was $$\$ 2,000$$and you deposit \(x\) amount in one investment, how can you represent the remaining amount?

How do we recognize when an equation, for example \(y=4 x+3,\) will be a straight line (linear) when graphed?

Describe in your own words what the \(y\) -intercept of a graph is.

When solving an inequality, we arrive at: $$\begin{array}{c} x+2>x+3 \\ 2>3 \end{array}$$ Explain what our solution set is.

Explain why \(|2 x+5|=-7\) has no solutions.

In the quadratic formula, what is the name of the expression under the radical sign \(b^{2}-4 a c\), and how does it determine the number of and nature of our solutions?

What is a characteristic of the plot of a real number in the complex plane?

If a man sawed a 10 -ft board into two sections and one section was \(n \mathrm{ft}\) long, how long would the other section be in terms of \(n\) ?

What does it mean when we say that a linear equation is inconsistent?

When using the distance formula \(d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\) explain the correct order of operations that are to be performed to obtain the correct answer.

Describe how to graph $$y=|x-3|$$.

Describe two scenarios where using the square root property to solve a quadratic equation would be the most efficient method.

For the following exercises, evaluate the algebraic expressions. If \(y=x^{2}+x-4,\) evaluate \(y\) given \(x=2 i\).

If Bill was traveling \(v \mathrm{mi} / \mathrm{h}\), how would you represent Daemon's speed if he was traveling \(10 \mathrm{mi} / \mathrm{h}\) faster?

When solving the following equation: \(\frac{2}{x-5}=\frac{4}{x+1}\) explain why we must exclude \(x=5\) and \(x=-1\) as possible solutions from the solution set.

For each of the following exercises, find the \(x\) -intercept and the \(y\) -intercept without graphing. Write the coordinates of each intercept. $$ y=-3 x+6 $$

For the following exercises, solve the inequality. Write your final answer in interval notation. $$ 4 x-7 \leq 9 $$

For the following exercises, solve the rational exponent equation. Use factoring where necessary. $$ x^{\frac{2}{3}}=16 $$

For the following exercises, solve the quadratic equation by factoring. $$ x^{2}+4 x-21=0 $$

For the following exercises, evaluate the algebraic expressions. If \(y=x^{3}-2,\) evaluate \(y\) given \(x=i\).

For the following exercises, use the information to find a linear algebraic equation model to use to answer the question being asked. Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is \(113 ?\)

For the following exercises, solve the equation for \(x\). $$ 7 x+2=3 x-9 $$

For each of the following exercises, find the \(x\) -intercept and the \(y\) -intercept without graphing. Write the coordinates of each intercept. $$ 4 y=2 x-1 $$

For the following exercises, solve the inequality. Write your final answer in interval notation. $$ 3 x+2 \geq 7 x-1 $$

For the following exercises, solve the rational exponent equation. Use factoring where necessary. $$ x^{\frac{3}{4}}=27 $$

For the following exercises, solve the quadratic equation by factoring. $$ x^{2}-9 x+18=0 $$

For the following exercises, evaluate the algebraic expressions. If \(y=x^{2}+3 x+5,\) evaluate \(y\) given \(x=2+i\).

For the following exercises, use the information to find a linear algebraic equation model to use to answer the question being asked. Beth and Ann are joking that their combined ages equal Sam's age. If Beth is twice Ann's age and Sam is 69 yr old, what are Beth and Ann's ages?

For the following exercises, solve the equation for \(x\). $$ 4 x-3=5 $$

For each of the following exercises, find the \(x\) -intercept and the \(y\) -intercept without graphing. Write the coordinates of each intercept. $$ 3 x-2 y=6 $$

For the following exercises, solve the inequality. Write your final answer in interval notation. $$ -2 x+3>x-5 $$

For the following exercises, solve the rational exponent equation. Use factoring where necessary. $$ 2 x^{\frac{1}{2}}-x^{\frac{1}{4}}=0 $$