Chapter 1

Solve equation using the quadratic formula. $$ x^{2}+8 x+12=0 $$

In Exercises 61–78, solve each absolute value equation or indicate that the equation has no solution. $$|2 x-3|=11$$

Solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. $$5 x+7=2 x+7$$

In Exercises 59–94, solve each absolute value inequality. $$ \left|\frac{2 x+6}{3}\right|<2 $$

Solve equation using the quadratic formula. $$ x^{2}+5 x+3=0 $$

In Exercises 61–78, solve each absolute value equation or indicate that the equation has no solution. $$2|3 x-2|=14$$

At the north campus of a performing arts school, 10% of the students are music majors. At the south campus, 90% of the students are music majors. The campuses are merged into one east campus. If 42% of the 1000 students at the east campus are music majors, how many students did the north and south campuses have before the merger?

determine whether each statement makes sense or does not make sense, and explain your reasoning. The rectangular coordinate system provides a geometric picture of what an equation in two variables looks like.

Solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. $$\frac{2 x}{x-3}=\frac{6}{x-3}+4$$

In Exercises 59–94, solve each absolute value inequality. $$ \left|\frac{3(x-1)}{4}\right|<6 $$

Solve equation using the quadratic formula. $$ x^{2}+5 x+2=0 $$

In Exercises 61–78, solve each absolute value equation or indicate that the equation has no solution. $$3|2 x-1|=21$$

The price of a dress is reduced by \(40 \% .\) When the dress still does not sell, it is reduced by 40 \% of the reduced price. If the price of the dress after both reductions is \(\$ 72,\) what was the original price?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. There is something wrong with my graphing utility because it is not displaying numbers along the \(x\) - and \(y\) -axes.

Solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. $$\frac{3}{x-3}=\frac{x}{x-3}+3$$

In Exercises 59–94, solve each absolute value inequality. $$ |x|>3 $$

Solve equation using the quadratic formula. $$ 3 x^{2}-3 x-4=0 $$

In Exercises 61–78, solve each absolute value equation or indicate that the equation has no solution. $$7|5 x|+2=16$$

In a film, the actor Charles Coburn plays an elderly “uncle” character criticized for marrying a woman when he is 3 times her age. He wittily replies, “Ah, but in 20 years time I shall only be twice her age.” How old is the “uncle” and the woman?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used the ordered pairs \((-2,2),(0,0),\) and \((2,2)\) to graph a straight line.

Combine the types of equations we have discussed in this section. Solve equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. $$\frac{x+5}{2}-4=\frac{2 x-1}{3}$$

In Exercises 59–94, solve each absolute value inequality. $$ |x|>5 $$

Solve equation using the quadratic formula. $$ 5 x^{2}+x-2=0 $$

In Exercises 61–78, solve each absolute value equation or indicate that the equation has no solution. $$7|3 x|+2=16$$

Suppose that we agree to pay you \(8 \notin\) for every problem in this chapter that you solve correctly and fine you 5 e for every problem done incorrectly. If at the end of 26 problems we do not owe each other any money, how many problems did you solve correctly?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I add or subtract complex numbers, I am basically combining like terms.

Combine the types of equations we have discussed in this section. Solve equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. $$\frac{x+2}{7}=5-\frac{x+1}{3}$$

In Exercises 59–94, solve each absolute value inequality. $$ |x-1| \geq 2 $$

Solve equation using the quadratic formula. $$ 4 x^{2}=2 x+7 $$

In Exercises 61–78, solve each absolute value equation or indicate that the equation has no solution. $$2\left|4-\frac{5}{2} x\right|+6=18$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Some irrational numbers are not complex numbers.

Combine the types of equations we have discussed in this section. Solve equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. $$\frac{2}{x-2}=3+\frac{x}{x-2}$$

In Exercises 59–94, solve each absolute value inequality. $$ |x+3| \geq 4 $$

Solve equation using the quadratic formula. $$ 3 x^{2}=6 x-1 $$

A thief steals a number of rare plants from a nursery. On the way out, the thief meets three security guards, one after another. To each security guard, the thief is forced to give one-half the plants that he still has, plus 2 more. Finally, the thief leaves the nursery with 1 lone palm. How many plants were originally stolen?

In Exercises 61–78, solve each absolute value equation or indicate that the equation has no solution. $$4\left|1-\frac{3}{4} x\right|+7=10$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \((3+7 i)(3-7 i)\) is an imaginary number.

Combine the types of equations we have discussed in this section. Solve equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. $$\frac{6}{x+3}+2=\frac{-2 x}{x+3}$$

In Exercises 59–94, solve each absolute value inequality. $$ |3 x-8|>7 $$

Solve equation using the quadratic formula. $$ x^{2}-6 x+10=0 $$

Solve for \(C: \quad V=C-\frac{C-S}{L} N\)

In Exercises 61–78, solve each absolute value equation or indicate that the equation has no solution. $$|x+1|+5=3$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ \frac{7+3 i}{5+3 i}=\frac{7}{5} $$

Combine the types of equations we have discussed in this section. Solve equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. $$8 x-(3 x+2)+10=3 x$$

In Exercises 59–94, solve each absolute value inequality. $$ |5 x-2|>13 $$

Solve equation using the quadratic formula. $$ x^{2}-2 x+17=0 $$

One of the best ways to learn how to solve a word problem in algebra is to design word problems of your own. Creating a word problem makes you very aware of precisely how much information is needed to solve the problem. You must also focus on the best way to present information to a reader and on how much information to give. As you write your problem, you gain skills that will help you solve problems created by others. The group should design five different word problems that can be solved using linear equations. All of the problems should be on different topics. For example, the group should not have more than one problem on simple interest. The group should turn in both the problems and their algebraic solutions.

In Exercises 61–78, solve each absolute value equation or indicate that the equation has no solution. $$|x+1|+6=2$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The ordered pair \((2,5)\) satisfies \(3 y-2 x=-4\).

Combine the types of equations we have discussed in this section. Solve equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. $$2(x+2)+2 x=4(x+1)$$