Chapter 1

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ x<5 \text { and } x>0 $$

Translate each verbal sentence into an equation, using \(x\) as the variable. Then solve the equation. $$ \text { When } 75 \% \text { of a number is added to } 6 \text { , the result is } 3 \text { more than the number. Find the number. } $$

Solve each formula for the specified variable. $$\begin{aligned}&A=P(1+r t) \text { for } t\\\&\text { (future value for simple interest) }\end{aligned}$$

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(5 x+2=3 x-6\)

Solve each equation. $$ |0.5 x|=6 $$

Solve each inequality. Graph the solution set, and write it using interval notation. \(-1.3 x \geq-5.2\)

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ x \leq 2 \text { and } x \leq 5 $$

Determine whether each is an expression or an equation. Simplify any expressions, and solve any equations. $$ 5(x+3)-8(2 x-6) $$

Two steamers leave a port on a river at the same time, traveling in opposite directions. Each is traveling \(22 \mathrm{mph}\). How long will it take for them to be \(110 \mathrm{mi}\) apart?

Solve each formula for the specified variable.$$\begin{aligned}&M=C(1+r) \text { for } r\\\&\text { (markup) }\end{aligned}$$

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(9 x+1=7 x-9\)

Solve each inequality. Graph the solution set, and write it using interval notation. \(-2.5 x \leq-1.25\)

Solve each equation. $$ |0.3 x|=9 $$

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ x \geq 3 \text { and } x \geq 6 $$

A train leaves Kansas City, Kansas, and travels north at \(85 \mathrm{~km}\) per \(\mathrm{hr}\). Another train leaves at the same time and travels south at \(95 \mathrm{~km}\) per hr. How long will it take before they are \(315 \mathrm{~km}\) apart?

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(7 x-5 x+15=x+8\)

Solve each inequality. Graph the solution set, and write it using interval notation. \(5 x+2 \leq-48\)

Solve each equation. $$ \left|\frac{1}{2} x+3\right|=2 $$

Determine whether each is an expression or an equation. Simplify any expressions, and solve any equations. $$ 5(x+3)-8(2 x-6)=12 $$

Mulder and Scully are driving to Georgia to investigate "Big Blue," a giant reptile reported in one of the local lakes. Mulder leaves the office at 8: 30 A.M. averaging 65 mph. Scully leaves at 9: 00 A.M., following the same path and averaging \(68 \mathrm{mph}\). At what time will Scully catch up with Mulder?

The formula \(F=\frac{9}{5} C+32\) can be solved for \(C\) to obtain \(C=\frac{5}{9}(F-32)\). Which one of the following is not equivalent to this? A. \(C=\frac{5}{9} F-\frac{160}{9}\) B. \(C=\frac{5 F}{9}-\frac{160}{9}\) C. \(C=\frac{5 F-160}{9}\) D. \(C=\frac{5}{9} F-32\)

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(2 x+4-x=4 x-5\)

Solve each inequality. Graph the solution set, and write it using interval notation. \(-2.5 x \leq-1.25\)

Solve each equation. $$ \left|\frac{2}{3} x-1\right|=5 $$

Determine whether each is an expression or an equation. Simplify any expressions, and solve any equations. $$ -7(x+4)+13(x-6)=18 $$

Solve each equation for \(y\). $$4 x+y=1$$

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(12 w+15 w-9+5=-3 w+5-9\)

Solve each equation. $$ \left|1+\frac{3}{4} x\right|=7 $$

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ x-3 \leq 6 \text { and } x+2 \geq 7 $$

Determine whether each is an expression or an equation. Simplify any expressions, and solve any equations. $$ \frac{1}{2} x-\frac{1}{6} x+\frac{3}{2}-8 $$

Solve each equation for \(y\). $$3 x+y=9$$

Solve each inequality. Graph the solution set, and write it using interval notation. \(\frac{5 x-6}{8}<8\)

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(-4 x+5 x-8+4=6 x-4\)

Solve each equation. $$ \left|2-\frac{5}{2} x\right|=14 $$

Determine whether each is an expression or an equation. Simplify any expressions, and solve any equations. $$ \frac{1}{3} x+\frac{1}{5} x-\frac{1}{2}+7 $$

Sharon commutes to her office by train. When she walks to the train station, it takes her 40 min. When she rides her bike, it takes her 12 min. Her average walking rate is 7 mph less than her average biking rate. Find the distance from her house to the train station. $$ \begin{array}{|l|l|l|l|} \hline & \text { Rate } & \text { Time } & \text { Distance } \\ \text { Walking } & & & \\ \text { Biking } & & & \\ \hline \end{array} $$

Solve each equation for \(y\). $$x-2 y=-6$$

Solve each inequality. Graph the solution set, and write it using interval notation. \(\frac{2 x-5}{-4}>5\)

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(3(2 t-4)=20-2 t\)

Solve each equation. $$ |0.02 x-1|=2.50 $$

Complete the six problem-solving steps to solve each problem. In 2015 , the corporations securing the most U.S. patents were IBM and Samsung. Together, the two corporations secured a total of 12,368 patents, with Samsung receiving 2250 fewer patents than IBM. How many patents did each corporation secure? (Data from U.S. Patent and Trademark Office.) Step 1 Read the problem carefully. We are asked to find ______ . 2 Assign a variable. Let \(x=\) the number of patents that IBM secured. Step Then \(x-2250=\) the number of ______ . Step 3 Write an equation. ____\(+ _____ \ldots=12,368\) Step 4 Solve the equation. \(x=\) ______ . \(\begin{array}{llll}\text { Step } 5 & \text { State the answer. } & \text { IBM secured } & \text { patents. Samsung secured } & \text { patents. }\end{array}\) Step 6 Check. The number of Samsung patents was _____ fewer than the number of _____ The total number of patents was \(7309+\) _____ \(= ______\).

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ -3 x>3 \text { and } x+3>0 $$

Johnny leaves Memphis to visit his cousin Anne, who lives in the town of Hornsby, Tennessee, 80 mi away. He travels at an average rate of 50 mph. One- half hour later, Anne leaves to visit Johnny, traveling at an average rate of \(60 \mathrm{mph}\). How long after Anne leaves will it be before they meet?

Solve each equation for \(y\). $$x-5 y=-20$$

Solve each inequality. Graph the solution set, and write it using interval notation. \(\frac{3 x-2}{-5}<6\)

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(2(3-2 x)=x-4\)

Solve each equation. $$ |0.04 x-3|=5.96 $$

On an automobile trip, Laura maintained a steady rate for the first two hours. Rush-hour traffic slowed her rate by 25 mph for the last part of the trip. The entire trip, a distance of \(125 \mathrm{mi},\) took \(2 \frac{1}{2} \mathrm{hr} .\) What was her rate during the first part of the trip?

Solve each problem. The John Hancock Center in Chicago has a rectangular base. The length of the base measures \(65 \mathrm{ft}\) less than twice the width. The perimeter of the base is \(860 \mathrm{ft}\). What are the dimensions of the base?

Solve each equation for \(y\). $$4 x+9 y=11$$