Chapter 1

Solve each equation, and check the solution. \(0.006(50-x)=0.272-0.004 x\)

According to some medical advisors, a body mass index (BMI) between 19 and 25 suggests a healthful weight. Use the formula $$ \mathrm{BMI}=\frac{704 \times(\text { weight in pounds })}{(\text { height in inches })^{2}} $$ to find the weight range \(w,\) to the nearest pound, that gives a healthful BMI for each height. (a) 72 in. (b) 63 in. (c) Your height in inches

Solve each equation or inequality. $$ |x+4|+1=2 $$

Solve each equation or inequality. $$ |x+5|-2=12 $$

Peripheral Visions, Inc., finds that the cost of producing \(x\) studio-quality DVDs is \(C=20 x+100,\) while the revenue produced from them is \(R=24 x(C\) and \(R\) in dollars).

Solve each equation or inequality. $$ |2 x+1|+3>8 $$

Solve the equation. Give the solution set. $$28=\frac{7}{2}(a+13)$$

Speedy Delivery finds that the cost of making \(x\) deliveries is \(C=3 x+2300,\) while the revenue produced from them is \(R=5.50 x(C\) and \(R\) in dollars).

Solve each equation or inequality. $$ |6 x-1|-2>6 $$

Solve the linear equation. Graph the solution set on a number line. $$ 5(x+3)-2(x-4)=2(x+7) $$

Solve each equation or inequality. $$ |x+5|-6 \leq-1 $$

Solve the linear inequality. Graph the solution set on a number line. $$ 5(x+3)-2(x-4)>2(x+7) $$

Solve each equation or inequality. $$ |x-2|-3 \leq 4 $$

Solve the linear inequality. Graph the solution set on a number line. $$ 5(x+3)-2(x-4)<2(x+7) $$

Solve each equation or inequality. $$ |0.1 x-2.5|+0.3 \geq 0.8 $$

Solve each equation or inequality. $$ |0.5 x-3.5|+0.2 \geq 0.6 $$

Complete the following: The solution set of \(-3(x+2)=3 x+12\) is ____. The solution set of \(-3(x+2)<3 x+12\) is ____. Therefore, the solution set of \(-3(x+2)>3 x+12\) is ____.

Solve each equation or inequality. $$ |0.5 x-3.5|+0.2 \geq 0.6 $$

Solve each equation or inequality. $$ \left|\frac{2}{3} x+\frac{1}{6}\right|+\frac{1}{2}=\frac{5}{2} $$

Solve each equation. $$ |3 x+1|=|2 x+4| $$

Solve each equation. $$ |7 x+12|=|x-8| $$

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

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

Solve each equation. $$ |2 x-6|=|2 x+11| $$

Solve each equation. $$ |3 x-1|=|3 x+9| $$

Solve each equation or inequality. $$ |x| \geq-15 $$

Solve each equation or inequality. $$ |4 x+1|=0 $$

Solve each equation or inequality. $$ |6 x-2|=0 $$

Solve each equation or inequality. $$ |x+5|>-9 $$

Solve each equation or inequality. $$ |7 x+3| \leq 0 $$

Solve each equation or inequality. $$ |4 x-1| \leq 0 $$

Solve each equation or inequality. $$ |5 x-2|=0 $$

Solve each equation or inequality. $$ |7 x+4|=0 $$

Solve each equation or inequality. $$ |x-2|+3 \geq 2 $$

Solve each equation or inequality. $$ |x-4|+5 \geq 4 $$

Solve each equation or inequality. $$ |10 x+7|+3<1 $$

Determine the number of ounces a filled carton of the given size may contain for the given relative error. $$ \left|\frac{x-x_{t}}{x_{t}}\right|=\text { relative error in } x $$ 64 -oz carton; relative error no greater than 0.05.

Determine the number of ounces a filled carton of the given size may contain for the given relative error. $$ \left|\frac{x-x_{t}}{x_{t}}\right|=\text { relative error in } x $$ 32-oz carton; relative error no greater than 0.02

Find the open interval in which \(x\) must lie in order for the given condition to hold. \(y=2 x+1,\) and the difference of \(y\) and 1 is less than 0.1 .

Find the open interval in which \(x\) must lie in order for the given condition to hold. \(y=4 x-6,\) and the difference of \(y\) and 2 is less than 0.02.

Find the open interval in which \(x\) must lie in order for the given condition to hold. \(y=4 x-8,\) and the difference of \(y\) and 3 is less than 0.001.

Find the open interval in which \(x\) must lie in order for the given condition to hold. \(y=5 x+12,\) and the difference of \(y\) and 4 is less than 0.0001.

Dr. Mosely has determined that \(99 \%\) of the babies he has delivered have weighed \(x\) pounds, where $$ |x-8.3|<1.5 $$ What range of weights corresponds to this inequality?

The Celsius temperatures \(x\) on Mars approximately satisfy the inequality $$ |x+85| \leq 55 $$ What range of temperatures corresponds to this inequality?

The recommended daily intake (RDI) of calcium for females aged \(19-50\) is \(1000 \mathrm{mg}\). Write this statement as an absolute value inequality, with \(x\) representing the RDI, to express the RDI plus or minus \(100 \mathrm{mg}\). Solve the inequality. (Data from National Academy of Sciences - Institute of Medicine.)

The average clotting time of blood is \(7.45 \mathrm{sec}\), with a variation of plus or minus \(3.6 \mathrm{sec}\). Write this statement as an absolute value inequality, with \(x\) representing the time. Solve the inequality.

The 10 tallest buildings in Houston, Texas, are listed along with their heights. $$ \begin{array}{|l|c|} \hline \quad {\text { Building }} & \text { Height (in feet) } \\ \hline \text { JPMorgan Chase Tower } & 1002 \\ \text { Wells Fargo Plaza } & 992 \\ \text { Williams Tower } & 901 \\ \text { Bank of America Center } & 780 \\ \text { Texaco Heritage Plaza } & 762 \\ \text { 609 Main at Texas } & 757 \\ \text { Enterprise Plaza } & 756 \\ \text { Centerpoint Energy Plaza } & 741 \\ \text { 1600 Smith St. } & 732 \\ \text { Fulbright Tower } & 725 \\ \hline \end{array} $$ Use this information To find the average of a group of numbers, we add the numbers and then divide by the number of numbers. Use a calculator to find the average of the heights.

The 10 tallest buildings in Houston, Texas, are listed along with their heights. $$ \begin{array}{|l|c|} \hline \quad {\text { Building }} & \text { Height (in feet) } \\ \hline \text { JPMorgan Chase Tower } & 1002 \\ \text { Wells Fargo Plaza } & 992 \\ \text { Williams Tower } & 901 \\ \text { Bank of America Center } & 780 \\ \text { Texaco Heritage Plaza } & 762 \\ \text { 609 Main at Texas } & 757 \\ \text { Enterprise Plaza } & 756 \\ \text { Centerpoint Energy Plaza } & 741 \\ \text { 1600 Smith St. } & 732 \\ \text { Fulbright Tower } & 725 \\ \hline \end{array} $$ Use this information. Let \(k\) represent the average height of these buildings. If a height \(x\) satisfies the inequality $$ |x-k|

The 10 tallest buildings in Houston, Texas, are listed along with their heights. $$ \begin{array}{|l|c|} \hline \quad {\text { Building }} & \text { Height (in feet) } \\ \hline \text { JPMorgan Chase Tower } & 1002 \\ \text { Wells Fargo Plaza } & 992 \\ \text { Williams Tower } & 901 \\ \text { Bank of America Center } & 780 \\ \text { Texaco Heritage Plaza } & 762 \\ \text { 609 Main at Texas } & 757 \\ \text { Enterprise Plaza } & 756 \\ \text { Centerpoint Energy Plaza } & 741 \\ \text { 1600 Smith St. } & 732 \\ \text { Fulbright Tower } & 725 \\ \hline \end{array} $$ Use this information. Work each of the following. (a) Write an absolute value inequality that describes the height of a building that is not within \(95 \mathrm{ft}\) of the average. (b) Solve the inequality from part (a). (c) Use the result of part (b) to list the buildings that are not within \(95 \mathrm{ft}\) of the average. (d) Confirm that the answer to part (c) makes sense by comparing it with the answer to Exercise 131 .