Chapter 1

Simplify each expression. $$-\frac{5}{9} y-\frac{7}{18} y$$

Solve each equation. $$ 5-\frac{x+2}{3}=7-x $$

Let \(a\) and \(b\) represent real numbers. Which of the following statements are always true? a. \(|a+b|=|a|+|b|\) b. \(|a \cdot b|=|a| \cdot|b|\) c. \(|a+b| \leq|a|+|b|\)

Simplify each expression. $$-2[4(z-9)-6(3 z-7)]-7(2 z-1)$$

Solve each equation. $$ 13.5 y+16.2=0 $$

Dietitians often calculate a patient’s BMI (Body Mass Index) to screen for weight categories that may lead to health problems. BMI is a number that is calculated from one’s weight and height. It is an indication of a person’s total body weight that comes from fat. The formula for BMI, as it appears in dietary textbooks, is: $$ \mathrm{BMI}=\frac{\text { weight }(\mathrm{lb}) \cdot 703}{\text { height }^{2}\left(\text { in } .^{2}\right)} $$ Solve the formula for weight. (IMAGE CANT COPY)

Evaluate each expression for the given values. See Example 10. $$ \begin{aligned} &\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \text { for } x_{1}=-2, x_{2}=4\\\ &y_{1}=4, y_{2}=-4 \end{aligned} $$

Simplify each expression. $$9\left(m^{3}+3\right)-5\left(3-m^{3}\right)-8\left(-1-m^{3}\right)$$

Surface Area. To find the amount of tin needed to make the coffee can shown in below, we use the formula for the surface area of a right circular cylinder, \(A=2 \pi r^{2}+2 \pi r h .\) Solve the formula for \(h\) (GRAPH CANT COPY)

Solve each equation. $$ \frac{7}{3} y+1=0 $$

Simplify each expression. $$21\left(\frac{6}{7} h^{2}-\frac{15}{21} h\right)+21\left(\frac{1}{3} h\right)$$

Explain the difference between what perimeter measures and what area measures.

Solve each equation. $$ \frac{4}{5}(x+5)=\frac{7}{8}(3 x+23)-7 $$

Evaluate each expression for the given values. See Example 10. $$ -n\left(4 n^{2}-27 m^{2}\right)^{3} \text { for } m=\frac{1}{3} \text { and } n=\frac{1}{2} $$

Simplify each expression. $$\frac{1}{12}(y-12 x)-\frac{1}{3}(y-3 x)$$

Solve each equation. $$ \frac{2}{3}(2 x+2)+4=\frac{1}{6}(5 x+29) $$

After solving a formula for \(m,\) a student compared her answer with that at the back of the textbook. Could this problem have two different-looking answers? Explain why or why not. $$ \begin{aligned} &\text { Student: } m=\frac{5}{9} a r+1\\\ &\text { Book: } m=\frac{5 a r+9}{9} \end{aligned} $$

Simplify each expression. $$4.3(y+9)-8.1 y$$

Solve each equation. $$ \frac{t-2}{5}+5 t=\frac{7}{5}-\frac{t-2}{2} $$

Explain the error made below. $$ T=\frac{a d x+\frac{1}{y}}{\frac{y}{1}} $$

Evaluate each expression. a. \(100-20+5\) b. \(100-(20+5)\) c. \(100 \div 20 \cdot 5\) d. \(100 \div(20 \cdot 5)\)

Simplify each expression. $$2.1(4+5 z)+0.9 z$$

A student solved \(x+5 c=3 c+a\) for \(c .\) His answer was \(c=\frac{3 c+a-x}{5} .\) Explain why the equation is not solved for \(c\)

Solve each equation. $$ \frac{2}{3}(3 m-2)=\frac{3}{4} m+\frac{11}{12} $$

Evaluate each expression. $$ \text { a. } 2 \cdot 3^{2} $$

Simplify each expression. $$3 x^{2}-\left(-2 x^{2}\right)-5 x^{2}$$

Solve each equation. $$ 6+4 t-1=6-15 t+12 t-8 $$

Simplify each expression. $$ (16 b+8)\left(\frac{5}{4}\right)-8 b $$

Evaluate each expression. a. Subtract \(-3.9\) from \(-11.2\) b. Subtract \(-11.2\) from \(-3.9\)

Simplify each expression. $$8 x^{3}-x^{3}-\left(-2 x^{3}\right)$$

Solve each equation. $$ 5 c-8-3 c=10+2 c-3 $$

Simplify each expression. $$ -7(a-3)-5[3(a-4)-2(a+2)] $$

Evaluate each expression. $$ \text { a. }(-2-\sqrt{64})^{2} \quad \text { b. }-2-(\sqrt{64})^{2} $$

Simplify each expression. $$19 a-\\{-2[4 a-2(a-16)]-3 a\\}$$

Simplify each expression and solve each equation. a. \(\frac{1}{2}(6 x+8)-10-\frac{2}{3}(6 x-9)\) b. \(\frac{1}{2}(6 x+8)-10=-\frac{2}{3}(6 x-9)\)

Simplify each expression. $$ -5.7 p t-p+5.1 p t+12 p $$

Simplify each expression. $$41 m-\\{-3[-2 m-7(m+1)]-6 m\\}$$

Simplify each expression and solve each equation. a. \(6.31 w+9.22+5(7.21 w-1.13)\) b. \(6.31 w+9.22=5(7.21 w-1.13)\)

Simplify each expression. $$ \frac{3}{5} t-\frac{2}{3} t $$

Simplify each expression. $$\frac{1}{2}(4 a-8)-6[2(5 a-1)-a]$$

Simplify each expression and solve each equation. a. \(-4\\{6 x-[3(7 x-1)-x]\\}+46 x\) b. \(-4\\{6 x-[3(7 x-1)-x]\\}=46 x\)

The highest and lowest temperatures ever recorded in several cities are shown in the table. List the cities in order, from the smallest to the largest range in temperature extremes. $$ \begin{array}{|l|c|c|} \hline \multirow{2}{*}\text { City } & \multicolumn{2}{|c|}\begin{array}{c} \text { Extreme } \\ \text { temperatures } \end{array} \\ \hline & \text { Highest } & \text { Lowest } \\ \hline \text { Atlanta, Georgia } & 105 & -8 \\ \hline \text { Boise, Idaho } & 111 & -25 \\ \hline \text { Helena, Montana } & 105 & -42 \\ \hline \text { New York, New York } & 107 & -3 \\ \hline \text { Omaha, Nebraska } & 114 & -23 \\ \hline \end{array} $$

Simplify each expression. $$\frac{1}{3}(6 t-9)-12[3(2 t-1)-t]$$

Simplify each expression and solve each equation. a. \(8[4-(5+6 r)]-8 r-11+2(4-12 r)\) b. \(8[4-(5+6 r)]-8 r=-11+2(4-12 r)\)

Solve \(d_{1} d_{2}=f d_{2}+f d_{1}\) for \(d_{1}\)

What does it mean to solve an equation?

a. \(-3(-4 t)(-2)\) b. \(-3(-4 t)-2\)

Evaluate \(2 a_{2}^{2}+3 a_{3}^{3}+4 a_{4}^{4}\) for \(a_{2}=2, a_{3}=3,\) and \(a_{4}=4\)

Why doesn't the equation \(x=x+1\) have a real-number solution?

a. \(6 a+6 a+6 a\) b. \(6 a+6 b+6 c\)