Chapter 1

Translate each verbal phrase into \(a\) mathematical expression using \(x\) as the variable. The product of 8 and 16 less than a number.

In Canada, \(\$ 1\) coins are called "loonies" because they have a picture of a loon on the reverse, and \(\$ 2\) coins are called "toonies." When Marissa returned home to San Francisco from a trip to Vancouver, she found that she had acquired 37 of these coins, with a total value of 51 Canadian dollars. How many coins of each denomination did she have?

Solve each equation. $$ |2 x+3|=19 $$

Let \(A=\\{1,2,3,4,5,6\\}, B=\\{1,3,5\\}, C=\\{1,6\\},\) and \(D=\\{4\\} .\) Find each set. $$ B \cup D $$

Determine whether each of the following is an expression or an equation. \(4(x+3)-2(x+1)+10\)

Translate each verbal phrase into \(a\) mathematical expression using \(x\) as the variable. The product of 8 more than a number and 5 less than the number.

Ahmad works at an ice cream shop. At the end of his shift, he counted the bills in his cash drawer and found 119 bills with a total value of \(\$ 347\). If all of the bills are \(\$ 5\) bills and \(\$ 1\) bills, how many of each denomination were in his cash drawer?

Solve each equation. $$ |4 x-5|=17 $$

Solve each formula for the specified variable. \(C=2 \pi r\) for \(r\) (circumference of a circle)

Let \(A=\\{1,2,3,4,5,6\\}, B=\\{1,3,5\\}, C=\\{1,6\\},\) and \(D=\\{4\\} .\) Find each set. $$ B \cup C $$

Determine whether each of the following is an expression or an equation. \(-10 x+12-4 x=-3\)

Translate each verbal phrase into \(a\) mathematical expression using \(x\) as the variable. The quotient of three times a number and 10.

Hussein collects U.S. gold coins. He has a collection of 41 coins. Some are \(\$ 10\) coins, and the rest are \(\$ 20\) coins. If the face value of the coins is \(\$ 540\), how many of each denomination does he have?

Solve each equation. $$ |5 x-1|=21 $$

Solve each formula for the specified variable. \(V=\pi r^{2} h\) for \(h\) (volume of a right circular cylinder)

Solve each inequality. Graph the solution set, and write it using interval notation. \(5 x+6<76\)

Let \(A=\\{1,2,3,4,5,6\\}, B=\\{1,3,5\\}, C=\\{1,6\\},\) and \(D=\\{4\\} .\) Find each set. $$ C \cup D $$

Determine whether each of the following is an expression or an equation. \(-10 x+12-4 x+3=0\)

Translate each verbal phrase into \(a\) mathematical expression using \(x\) as the variable. The quotient of 9 and five times a nonzero number.

In the 19 th century, the United States minted two-cent and three-cent pieces. Frances has three times as many three-cent pieces as two-cent pieces, and the face value of these coins is \(\$ 2.42 .\) How many of each denomination does she have?

Solve each equation. $$ |2 x+5|=14 $$

This incorrect solution contains a common error. \(\begin{aligned} 8 x-2(2 x-3) &=3 x+7 \\ 8 x-4 x-6 &=3 x+7 \text { Distributive property }\\\ &4 x-6=3 x+7 \quad \text {Combine like terms}\\\ &x=13 \quad \text {Subtract 3 x . Add 6} . \end{aligned}\) WHAT WENT WRONG? Give the correct solution.

Solve each inequality. Graph the solution set, and write it using interval notation. \(4 x<-16\)

Translate each verbal sentence into an equation, using \(x\) as the variable. Then solve the equation. $$ \text { The sum of a number and } 6 \text { is }-31 \text { . Find the number. } $$

In 2018, general admission to the Art Institute of Chicago cost \(\$ 25\) for adults and \(\$ 19\) for children and seniors. If \(\$ 32,972\) was collected from the sale of 1460 general admission tickets, how many adult tickets were sold? (Data from www.artic.edu)

Solve each formula for the specified variable. \(V=\frac{1}{3} \pi r^{2} h\) for \(h \quad\) (volume of a cone)

Solve each equation. $$ |2 x-9|=18 $$

Solve each inequality. Graph the solution set, and write it using interval notation. \(2 x>-10\)

Translate each verbal sentence into an equation, using \(x\) as the variable. Then solve the equation. $$ \text { The sum of a number and }-4 \text { is } 18 \text { . Find the number. } $$

For a high school production of Hello, Dolly!, student tickets cost \(\$ 5\) each and nonstudent tickets cost \(\$ 8\) each. If 480 tickets were sold and a total of \(\$ 2895\) was collected, how many tickets of each type were sold?

Concept Check Suppose we solve a linear equation and obtain, as our final result, an equation in Column I. Match each result with the solution set in Column II for the original equation. \(\mathbf{I}\) (a) \(7=7\) (b) \(x=0\) (c) \(7=0\) \(\mathbf{II}\) A. \(\\{0\\}\) B. \(\\{\) all real numbers \(\\}\) C. \(\varnothing\)

Solve each formula for the specified variable. $$\begin{aligned}&F=\frac{9}{5} C+32 \text { for } C\\\&\text { (Celsius to Fahrenheit) }\end{aligned}$$

Solve each equation. $$ |-3 x+8|=1 $$

Solve each inequality. Graph the solution set, and write it using interval notation. \(-4 x<16\)

Translate each verbal sentence into an equation, using \(x\) as the variable. Then solve the equation. If the product of a number and -4 is subtracted from the number, the result is 9 more than the number. Find the number.

Which one of the following linear equations does not have solution set \(\\{\) all real numbers \(\\} ?\) A. \(4 x=5 x-x\) B. \(3(x+4)=3 x+12\) C. \(4 x=3 x\) D. \(\frac{3}{4} x=0.75 x\) E. \(4(x-2)=2(2 x-4)\) F. \(2 x+18 x=20 x\)

Solve each formula for the specified variable. $$\begin{aligned}&C=\frac{5}{9}(F-32) \text { for } F\\\&\text { (Fahrenheit to Celsius) }\end{aligned}$$

Solve each equation. $$ |-6 x+5|=4 $$

Solve each inequality. Graph the solution set, and write it using interval notation. \(-5 x>25\)

Translate each verbal sentence into an equation, using \(x\) as the variable. Then solve the equation. If the quotient of a number and 6 is added to twice the number, the result is 8 less than the number. Find the number.

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(7 x+8=1\)

Solve each formula for the specified variable.\(a x+b=0\)(linear equation in \(x\) ) (a) for \(x\) (b) for \(a\)

Solve each equation. $$ \left|12-\frac{1}{2} x\right|=6 $$

Solve each inequality. Graph the solution set, and write it using interval notation. \(-\frac{3}{4} x \geq 30\)

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ x<2 \text { and } x>-3 $$

Translate each verbal sentence into an equation, using \(x\) as the variable. Then solve the equation. $$ \text { When } \frac{2}{3} \text { of a number is subtracted from } 12, \text { the result is } 10 . \text { Find the number. } $$

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(5 x-4=21\)

Solve each formula for the specified variable. \(y=m x+b\) (slope-intercept form of a linear equation) (a) for \(x\) (b) for \(m\)

Solve each equation. $$ \left|14-\frac{1}{3} x\right|=8 $$

Solve each inequality. Graph the solution set, and write it using interval notation. \(-\frac{2}{3} x \leq 12\)