Chapter 1

As of 2017 , the highest temperature ever recorded in the state of Washington was \(42^{\circ} \mathrm{C}\). Find the corresponding Fahrenheit temperature to the nearest degree.

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

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ x+2>7 \text { or } 1-x>6 $$

Solve each problem involving consecutive integers. Find three consecutive integers such that the sum of the first and twice the second is 17 more than twice the third.

As of \(2017,\) the lowest temperature ever recorded in South Dakota was \(-41^{\circ} \mathrm{F}\). Find the corresponding Celsius temperature to the nearest degree.

Solve each inequality. Graph the solution set, and write it using interval notation. \(\frac{3}{5}(t-2)-\frac{1}{4}(2 t-7) \leq 3\)

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(4(2 x+7)=2 x+25+3(2 x+1)\)

Solve each problem involving consecutive integers. Find three consecutive integers such that the sum of the first and twice the third is 39 more than twice the second.

Solve each percent problem. In \(2013,\) mobile messaging service WhatsApp had 300 million monthly active users worldwide. By \(2017,\) this number had increased \(333.3 \% .\) To the nearest million, what was the number of WhatsApp monthly active users worldwide in \(2017 ?\)

The base of the Great Pyramid of Cheops is a square whose perimeter is \(920 \mathrm{~m}\). What is the length of each side of this square?

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

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

Solve each problem involving consecutive integers. Find four consecutive integers such that the sum of the first three is 54 more than the fourth.

Solve each percent problem. On Major League Baseball Opening Day \(2016,\) the payroll of the Cleveland Indians was \(\$ 87.2\) million. In 2017 , it had increased \(44.3 \%\). To the nearest tenth of a million, what was the opening-day payroll of the Indians for \(2017 ?\)

Marina City in Chicago is a complex of two residential towers that resemble corncobs. Each tower has a concrete cylindrical core with a 35 -ft diameter and is \(588 \mathrm{ft}\) tall. Find the volume of the core of one of the towers to the nearest whole number.

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

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(4[2 x-(3-x)+5]=-(2+7 x)\)

Solve each compound inequality. Graph the solution set, and write it using interval notation. $$ -2 x+1>-11 \text { or } x+1>10 $$

Solve each problem involving consecutive integers. Find four consecutive integers such that the sum of the last three is 86 more than the first.

The circumference of a circle is \(480 \pi\) in. (a) What is its radius? (b) What is its diameter?

Solve each inequality. Graph the solution set, and write it using interval notation. \(8\left(\frac{1}{2} x+3\right)<8\left(\frac{1}{2} x-1\right)\)

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(-[2 x-(5 x+2)]=2+(2 x+7)\)

Solve each compound inequality. Graph the solution set, and write it using interval notation.$$ 4 x+1 \geq-7 \text { or }-2 x+3 \geq 5 $$

Solve each problem involving consecutive integers. If I add my current age to the age I will be next year on this date, the sum is 103 yr. How old will \(I\) be 10 yr from today?

Solve each percent problem. In \(2016,\) the average cost of a Thanksgiving turkey was \(\$ 22.74 .\) This price had decreased by \(1.58 \%\) in \(2017 .\) What was the average cost of a Thanksgiving turkey in \(2017 ?\)

The radius of a circle is 2.5 in. (a) What is its diameter? (b) What is its circumference?

Solve each inequality. Graph the solution set, and write it using interval notation. \(10\left(\frac{1}{5} x+2\right)<10\left(\frac{1}{5} x+1\right)\)

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(-[6 x-(4 x+8)]=9+(6 x+3)\)

Solve each compound inequality. Graph the solution set, and write it using interval notation.$$ 3 x+2 \leq-7 \text { or }-2 x+1 \leq 9 $$

Solve each problem involving consecutive integers. If I add my current age to the age I will be next year on this date, the sum is 129 yr. How old will \(I\) be 5 yr from today?

Solve each percent problem. At the end of a day, Lawrence found that the total cash register receipts at the motel where he works were \(\$ 2725 .\) This included the \(9 \%\) sales tax charged. Find the amount of tax.

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

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

Express each set in simplest interval form. (Hint: Graph each set and look for the intersection or union.) $$ (-\infty,-1] \cap[-4, \infty) $$

Solve each problem involving consecutive integers. Find three consecutive even integers such that the sum of the least integer and the middle integer is 26 more than the greatest integer.

Solve each percent problem. David sold his house for \(\$ 159,000\). He got this amount knowing that he would have to pay a \(6 \%\) commission to his agent. What amount did he have after the agent was paid?

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

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(4(x+2)-8 x-5=-3 x+9-2(x+6)\)

Express each set in simplest interval form. (Hint: Graph each set and look for the intersection or union.) $$ [-1, \infty) \cap(-\infty, 9] $$

Solve each problem involving consecutive integers. Find three consecutive even integers such that the sum of the least integer and the greatest integer is 12 more than the middle integer.

Solve each percent problem. Why is it impossible to mix candy worth \(\$ 4\) per \(1 \mathrm{~b}\) and candy worth \(\$ 5\) per Ib to obtain a final mixture worth \(\$ 6\) per \(1 \mathrm{~b} ?\)

12 is what percent of \(48 ?\)

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

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(7[2-(3+4 x)]-2 x=-9+2(1-15 x)\)

Express each set in simplest interval form. (Hint: Graph each set and look for the intersection or union.) $$ (-\infty,-6] \bigcap[-9, \infty) $$

Solve each problem involving consecutive integers. Find three consecutive odd integers such that the sum of the least integer and the middle integer is 19 more than the greatest integer.

Solve each percent problem. Write an equation based on the following problem, solve the equation, and explain why the problem has no solution. How much \(30 \%\) acid should be mixed with \(15 \mathrm{~L}\) of \(50 \%\) acid to obtain a mixture that is \(60 \%\) acid?

15 is what percent of \(150 ?\)

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

Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction. \(4[6-(1+2 x)]+10 x=2(10-3 x)+8 x\)