Chapter 3

Solve the equation. $$ 2(2 x+3)=-6(x+9) $$

Solve the equation by simplifying first. $$ 12-5=n+7 $$

Graph the numbers on a number line.Then write two inequalities that compare the numbers. $$-6,3$$

Solve the equation. \(-x+(5 x-7)=-5\)

Write the numbers in order from least to greatest. (Skills Review p. 770) $$217,2017,270,2170,2701$$

Use the table. It shows all the activity in a checking account during June. Deposits are positive and withdrawals are negative. $$ \begin{array}{|c|c|} \hline \text { Day } & {\text { Activity }} \\ \hline \text { June 6 } & {-\$ 225.00} \\ \hline \text { June 10 } & {+\$ 310.25} \\ \hline \text { June 17} & {+\$ 152.33} \\ \hline \text { June 25 } & {-\$ 72.45} \\ \hline \text { June 30 } & {-\$ 400.00} \\ \hline \end{array} $$ Find the total amount withdrawn in June.

MAIL DELIVERY Each household in the United States receives about 676 pieces of junk mail per year. If there are 52 weeks in a year, then about how many pieces of junk mail does a household receive per week? HINT: Let \(x=\) the number of pieces of junk mail received per week. Solve the equation \(52 x=676\)

Solve the equation. $$ 7-(-4 t)=4 t-14-21 t $$

Solve the equation by simplifying first. $$ -3=a+(-4) $$

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$-7 a-9=6$$

Solve the equation. \(5 a-(2 a-1)=-2\)

Write the numbers in order from least to greatest. (Skills Review p. 770) $$23.5,23.45,23.4,23.53,23.25$$

Which inverse operation can be used to solve the equation \(6+x=15 ?\) A) Add 6 to each side. B) Subtract 6 from each side. C) Multiply each side by 6. D) Divide each side by 6.

Use the table. It shows all the activity in a checking account during June. Deposits are positive and withdrawals are negative. $$ \begin{array}{|c|c|} \hline \text { Day } & {\text { Activity }} \\ \hline \text { June 6 } & {-\$ 225.00} \\ \hline \text { June 10 } & {+\$ 310.25} \\ \hline \text { June 17} & {+\$ 152.33} \\ \hline \text { June 25 } & {-\$ 72.45} \\ \hline \text { June 30 } & {-\$ 400.00} \\ \hline \end{array} $$ What was the total change in the account balance over the course of the month?

You can tell about how many miles you are from a thunderstorm by counting the seconds between seeing the lightning and hearing the thunder, and then dividing by five. How many seconds would you count for a thunderstorm that is nine miles away?

Solve the equation. $$ -\frac{3}{4} x+5=\frac{1}{4} x-3 $$

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$10-3 x=4 x$$

Which is a solution to the equation \(9 x-5 x-19=21 ?\) A) \(-10\) B) \(-\frac{1}{2}\) C) \(\frac{1}{2}\) D) 10

Write the numbers in order from least to greatest. (Skills Review p. 770) $$5.09,5.9,5.1,5.19,5.91$$

Solve \(\frac{1}{3}(7 x+5)=3 x-5\) \((f)-5\) \((0)-\frac{5}{2}\) (H) 10 (J) 15

Make an input-output table for the function \(A=8+5 t .\) Use \(2,3,4,5,\) and 6 as values for \(t\)

Solve the equation. $$ 7-\frac{1}{3} x=\frac{2}{3} x+4 $$

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$5 x+14=-x$$

The bill (parts and labor) for the repair of a car is \(\$ 458 .\) The cost of parts is \(\$ 339 .\) The cost of labor is \(\$ 34\) per hour. Which equation could you use to find the number of hours of labor? F) \(34(x+339)=458\) G) \(34+339 x=458\) H) \(34 x+339=458\) J) \(34+x+339=458\)

Find the product. $$ 6(-6) $$

Find the opposite of the number. $$ 8 $$

MULTIPLE CHOICE Which operation would you use to solve \(\frac{1}{4}=-8 x ?\) A. Divide by 4. B. Divide by \(-8\) C. Multiply by \(-8 .\) D. Multiply by 4

In Exercises 54–56, match the real-life problem with an equation. Then solve the problem. A. \(x+15=7\) B. \(15-x=7\) C. \(15+7=x\) D. \(x+15=-7\) You own \(15 \mathrm{CDs} .\) You buy 7 more. How many \(\mathrm{CDs}\) do you own now?

Which equations are equivalent? I. \(3 x-4 x+18=5 x\) II . \(4+6 x=8 x-2\) III. \(2 x-8=7-x\) (A) I and II \(\quad\) (B) II and III \(\quad\) C All \(\quad\) (D) None

What is the width of a rectangular soccer field that has an area of 9000 square feet and a length of 120 feet?

Write the expression in exponential form. \(a \cdot a \cdot a \cdot a \cdot a \cdot a\)

Find the product. $$ -3(-12) $$

Find the opposite of the number. $$ -3 $$

MULTIPLE CHOICE Solve \(-\frac{5}{7} x=-2\). F. \(\frac{14}{5}\) G. \(-\frac{14}{5}\) H. \(\frac{10}{7}\) J. \( \frac{7}{5}\)

For which equation is \(j=4\) a solution? $$ \begin{aligned} &\text{(F)}\quad -10+5 j=-2+2 j &\text{(G)}\quad 7 j-3 j+2=4 j-2\\\ &\text{(H)}\quad 6 j-4=4 j+4 &\text{(J)}\quad 63 j+7=2 j-2 \end{aligned} $$

In Exercises 54–56, match the real-life problem with an equation. Then solve the problem. A. \(x+15=7\) B. \(15-x=7\) C. \(15+7=x\) D. \(x+15=-7\) There are 15 members of a high school band brass section. After graduation there are only 7 members. How many members graduated?

Find the least common denominator of the pair of fractions. $$\frac{3}{4}, \frac{2}{5}$$

Write the expression in exponential form. \(x\) to the fifth power

Find the product. $$ -8(-5) $$

Find the opposite of the number. $$ 0.2 $$

MULTIPLE CHOICE Which equations are equivalent? I. \(\frac{3}{5} x=3\) II. \(\frac{x}{5}=2\) III. \(2 x=10\) VI. \(-x=-5\) A. I and II B. II and IV C. I, II, and III D. I, III, and IV

Solve \(15 x+6-x=16 x+6-2 x\) $$ \begin{array}{\underline{\phantom{xx}}}{ (A) \text { \(x=0\) }} \quad {(B) \text { \(x=6\) }} \quad{(C) \text { No solution }}\quad {(D) \text { Identity }} \end{array} $$

In Exercises 54–56, match the real-life problem with an equation. Then solve the problem. A. \(x+15=7\) B. \(15-x=7\) C. \(15+7=x\) D. \(x+15=-7\) The temperature rose 15 degrees to \(7^{\circ} \mathrm{F}\). What was the original temperature?

Find the least common denominator of the pair of fractions. $$\frac{2}{9}, \frac{3}{18}$$

Write the expression in exponential form. \(4 \cdot 4 \cdot 4\)

Find the product. $$ 11(-7) $$

Find the opposite of the number. $$ \frac{4}{5} $$

SIMPLIFYING EXPRESSIONS Simplify the expression. (Lesson 2.7) $$ 15-8 x+12 $$

It takes you 3 hours to drive to your friend's house at an average speed of 48 miles per hour. How far did you travel?

Turner Field in Atlanta, Georgia, has 49, 831 seats. Jacobs Field in Cleveland, Ohio, has \(43,368\) seats. How many seats need to be added to Jacobs Field for it to have as many seats as Turner Field?