Chapter 1

Simplify by combining like terms. See Example 5 . $$0.7 h-3.8 h$$

Evaluate each expression. See Example \(8 .\) $$ 4 \cdot 2^{3} $$

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ -7.999 \quad-7.1 $$

When discussing weight management with their patients, dietitians stress the importance of limiting calorie intake and increasing physical activity. One method dietitians use to determine if a patient has a daily calorie surplus (or deficit) is to subtract the patient's daily resting metabolic rate and the calories that he/she burns during physical activity that day from the calories he/she ingests that day. Translate this verbal model into a mathematical model.

Simplify by combining like terms. See Example 5 . $$-5.7 m+5.3 m$$

Evaluate each expression. See Example \(8 .\) $$ 4 \cdot 5^{3} $$

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ 4 \frac{1}{2} \quad \frac{7}{2} $$

Solve each equation. If the equation is an identity or a contradiction, so indicate. See Example 9. $$ 8 x+3(2-x)=5 x+6 $$

Simplify by combining like terms. See Example 5 . $$1.8 x^{2}-5.1 x^{2}+4.1 x^{2}$$

Solve for the specified variable. $$ y=m x+b \quad \text { for } x $$

Evaluate each expression. See Example \(8 .\) $$ -12 \div 3 \cdot 2 $$

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ \frac{3}{5} \quad 0.06 $$

Use the data in each table to find an equation that mathematically describes the relationship between the two quantities. $$ \begin{array}{|c|c|} \hline \text { Tower height (ft) } & \text { Height of base (ft) } \\ \hline 15.5 & 5.5 \\ \hline 22 & 12 \\ \hline 25.25 & 15.25 \\ \hline 45.125 & 35.125 \\ \hline \end{array} $$

Simplify by combining like terms. See Example 5 . $$3.7 x^{2}+3.3 x^{2}-1.1 x^{2}$$

Solve each equation. If the equation is an identity or a contradiction, so indicate. See Example 9. $$ 4(2-3 t)+6 t=-6 t+8 $$

Solve for the specified variable. $$ P=2 l+2 w \quad \text { for } l $$

Evaluate each expression. See Example \(8 .\) $$ -18 \div 6 \cdot 3 $$

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ \frac{21}{50} \quad 0.4 $$

Use the data in each table to find an equation that mathematically describes the relationship between the two quantities. $$ \begin{array}{|c|c|} \hline \text { Seasonal employees } & \text { Employees } \\ \hline 25 & 75 \\ \hline 50 & 100 \\ \hline 60 & 110 \\ \hline 80 & 130 \\ \hline \end{array} $$

Solve each equation. $$ 9 x=6 x $$

Simplify by combining like terms. See Example 5 . $$-8 x+5 x-(-x)$$

Solve each equation. If the equation is an identity or a contradiction, so indicate. See Example 9. $$ 2(x-3)=\frac{3}{2}(x-4)+\frac{x}{2} $$

Solve for the specified variable. $$ L=2 d+3.25(r+R) \quad \text { for } R $$

Evaluate each expression. See Example \(8 .\) $$ 7^{2}-(-9)^{2} $$

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ -\frac{11}{15} \quad-0.73 $$

Explain the difference between an expression and an equation. Give examples.

Solve each equation. $$ 7 a+2=12-4(a-3) $$

Simplify by combining like terms. See Example 5 . $$-20 y+3 y-(-6 y)$$

Solve each equation. If the equation is an identity or a contradiction, so indicate. See Example 9. $$ y+\frac{1}{2}=\frac{5}{2}(0.2 y+1)-\frac{1}{2}(4-y) $$

Solve for the specified variable. $$ l=\frac{a-S+S r}{r} \quad \text { for } a $$

Evaluate each expression. See Example \(8 .\) $$ 4^{2}-(-8)^{2} $$

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ -\frac{7}{30} \quad-0.23 $$

Use each word below in a sentence that indicates a mathematical operation. If you are unsure of the meaning of a word, look it up in a dictionary. $$\begin{array}{llll}\text { quadrupled } & \text { deleted } & \text { bisected } & \text { garnished } \\ \text { confiscated } & \text { annexed } & \text { docked } & \text { quintupled }\end{array}$$

Solve each equation. $$ \frac{8(y-5)}{3}=2(y-4) $$

Solve each equation. If the equation is an identity or a contradiction, so indicate. See Example 10. $$ 2 x-6=-2 x+4(x-2) $$

Simplify by combining like terms. See Example 5 . $$\frac{2}{5} a b-\left(-\frac{1}{2} a b\right)$$

Solve for the specified variable. $$ s=\frac{1}{2} g t^{2}+v t \quad \text { for } g $$

Evaluate each expression. See Example \(9 .\) $$ (4+2 \cdot 3)^{4} $$

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ \frac{27}{22} \quad 1.2 \overline{28} $$

Use each of the variables \(a, b, c,\) and \(d\) only once to write: a. a sum of two differences b. a difference of two sums

Solve each equation. $$ \frac{t-1}{3}=\frac{t+2}{6}+2 $$

Solve each equation. If the equation is an identity or a contradiction, so indicate. See Example 10. $$ 3(x-4)+6=-2(x+4)+5 x $$

Solve for the specified variable. $$ K=\frac{M v_{0}^{2}+I w^{2}}{2} \quad \text { for } I $$

Evaluate each expression. See Example \(9 .\) $$ |9-5(1-8)| $$

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ \frac{25}{990} \quad 0.0 \overline{26} $$

\(A\) student had a score of \(70 \%\) on a test that contained 30 questions. To improve his score, the instructor agreed to let him work 15 additional questions. How many of those must he get right to raise his grade to \(80 \% ?\)

Solve each equation. If the equation is an identity or a contradiction, so indicate. See Example 10. $$ -3 x=-2 x+1-(5+x) $$

Simplify by combining like terms. See Example 5 . $$\frac{3}{5} t+\frac{1}{3} t$$

Solve for the specified variable. $$ y-y_{1}=m\left(x-x_{1}\right) \quad \text { for } x $$

Evaluate each expression. See Example \(9 .\) $$ (-3-\sqrt{25})^{2} $$