Chapter 1

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |x|>3 $$

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ 3 x-4 \leq 8 \text { and }-4 x+1 \geq-15 $$

Solve each problem. The John Hancock Center tapers as it rises. The top floor is rectangular and has perimeter \(520 \mathrm{ft}\). The width of the top floor measures \(20 \mathrm{ft}\) more than one-half its length. What are the dimensions of the top floor?

Solve each equation for \(y\). $$7 x+8 y=11$$

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |x|>5 $$

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(5(x+3)+4 x-5=4-2 x\)

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ 7 x+6 \leq 48 \text { and }-4 x+3 \geq-21 $$

Solve each problem. Grant Wood painted his most famous work, American Gothic, in 1930 on composition board with perimeter 108.44 in. If the rectangular painting is 5.54 in. taller than it is wide, find the dimensions of the painting. (Data from The Gazette.)

Solve each equation for \(y\). $$-3 x+2 y=5$$

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(-2 x+5 x-9=3(x-4)-5\)

Solve each problem. The perimeter of a certain rectangle is 16 times the width. The length is \(12 \mathrm{~cm}\) more than the width. Find the length and width of the rectangle.

Solve each equation for \(y\). $$-5 x+3 y=12$$

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |x| \geq 6 $$

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(-6 x+2 x-11=-2(2 x-3)+4\)

Solve each problem. The Bermuda Triangle supposedly causes trouble for aircraft pilots. It has a perimeter of \(3075 \mathrm{mi}\). The shortest side measures 75 mi less than the middle side, and the longest side measures 375 mi more than the middle side. Find the lengths of the three sides.

Solve each equation for \(y\). $$6 x-5 y=7$$

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(-2(x+3)=-6(x+7)\)

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |r+5| \geq 20 $$

Solve each problem. The Vietnam Veterans Memorial in Washington, \(D C\), is in the shape of two sides of an isosceles triangle. If the two walls of equal length were joined by a straight line of \(438 \mathrm{ft}\), the perimeter of the resulting triangle would be \(931.5 \mathrm{ft}\). Find the lengths of the two walls. (Data from pamphlet obtained at Vietnam Veterans Memorial.)

Solve each equation for \(y\). $$8 x-3 y=4$$

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |x+4| \geq 8 $$

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(-4(x-9)=-8(x+3)\)

Solve each problem. The two companies with top revenues in the Fortune 500 list for 2016 were Walmart and Berkshire Hathaway. Their revenues together totaled \(\$ 710.5\) billion. Berkshire Hathaway revenues were \(\$ 263.3\) billion less than those of Walmart. What were the revenues of each corporation? (Data from Fortune magazine,

Solve each equation for \(y\). $$\frac{1}{2} x-\frac{1}{3} y=1$$

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |5 x+2|>10 $$

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ x \leq 1 \quad \text { or } \quad x \leq 8 $$

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(3(2 x+1)-2(x-2)=5\)

Solve each problem. On a particular day in \(2017,\) two of the longest-running Broadway shows were The Phantom of the Opera and Chicago. Together, there were 20.721 performances of these two shows during their Broadway runs. There were 3675 fewer performances of Chicago than of The Phantom of the Opera. How many performances were there of each show? (Data from The Broadway League.).

Solve each equation for \(y\). $$\frac{2}{3} x-\frac{2}{5} y=2$$

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |4 x+1| \geq 21 $$

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(4(x-2)+2(x+3)=6\)

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ x \geq 1 \quad \text { or } \quad x \geq 8 $$

Solve each problem. Galileo Galilei conducted experiments involving Italy's famous Leaning Tower of Pisa to investigate the relationship between an object's speed of fall and its weight. The Leaning Tower is \(804 \mathrm{ft}\) shorter than the Eiffel Tower in Paris, France. The two towers have a total height of \(1164 \mathrm{ft}\). How tall is each tower? (Data from The World Almanac and Book of Facts.).

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

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

Solve each problem. In 2017 , the Los Angeles Dodgers and the New York Yankees had the highest payrolls in Major League Baseball. The Dodgers' payroll was \(\$ 40.6\) million more than the Yankees' payroll, and the two payrolls totaled \(\$ 443.6\) million. What was the payroll for each team?

In \(2007,\) rain shortened the Indianapolis 500 race to \(415 \mathrm{mi}\). It was won by Dario Franchitti, who averaged \(151.774 \mathrm{mph}\). What was his time to the nearest thousandth?

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |5-x|>3 $$

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(6 x-3(5 x+2)=4(1-x)\)

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

Solve each problem. In \(2017,\) two popular brands on Instagram were National Geographic and Nike. National Geographic had 8.0 million more followers than Nike. Together, the two brands had 158.8 million followers. How many followers did each brand have?

Nora traveled from Kansas City to Louisville, a distance of \(520 \mathrm{mi}\), in \(10 \mathrm{hr}\). Find her rate in miles per hour.

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(6 x-4(3-2 x)=5(x-4)-10\)

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |-5 x+3| \geq 12 $$

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ x \geq-2 \quad \text { or } \quad x \leq 4 $$

Solve each problem. Ted Williams and Rogers Hornsby were two great hitters in Major League Baseball. Together, they had 5584 hits in their careers. Hornsby had 276 more hits than Williams. How many hits did each have?

The distance from Melbourne to London is \(10,500 \mathrm{mi}\). If a jet averages 500 mph between the two cities, what is its travel time in hours?

Solve each inequality. Graph the solution set, and write it using interval notation. $$ |-2 x-4| \geq 5 $$

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

Solve each problem. In \(2015,\) the number of graduating seniors taking the ACT exam was \(1,924,436 .\) In 2011 . a total of 1,617,173 graduating seniors took the exam. By what percent did the number increase over this period of time, to the nearest tenth of a percent?