Chapter 2

Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. Nine times a number is 30 more than three times that number. Find the number.

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$-21=y-4$$

Use the formulas for the area and circumference of a circle in Table 2.4 on page 170. Find the area and circumference of each circle. Express answers in terms of \(\pi .\) Then round to the nearest whole number. The circumference of a circle is \(16 \pi\) inches. Find the circle's radius and diameter.

Express the solution set of each inequality in interval notation and graph the interval. \(x \leq 1\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(p=15+\frac{5 d}{11}\) for \(d\)

Solve each equation in using the multiplication property of equality. Be sure to check your proposed $$28=-\frac{7}{2} x$$

Solve each equation. Be sure to check your proposed solution by substituting it for the variable in the original equation. $$3(x+2)=x+30$$

Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. Nine times a number is 30 more than three times that number. Find the number.

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$7+z=11$$

Express the solution set of each inequality in interval notation and graph the interval. \(x<4\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(A=\frac{1}{2}(a+b)\) for \(a\)

Solve each equation in using the multiplication property of equality. Be sure to check your proposed $$20=-\frac{5}{8} x$$

Solve each equation. Be sure to check your proposed solution by substituting it for the variable in the original equation. $$3(5-x)=4(2 x+1)$$

Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. If the quotient of three times a number and four is decreased by three, the result is nine. Find the number.

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$18+z=14$$

Express the solution set of each inequality in interval notation and graph the interval. \(x<5\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(A=\frac{1}{2}(a+b)\) for \(b\)

Solve each equation in using the multiplication property of equality. Be sure to check your proposed $$-x=17$$

Solve each equation. Be sure to check your proposed solution by substituting it for the variable in the original equation. $$3(3 x-1)=4(3+3 x)$$

Use the five-step strategy to solve each problem. How will you spend your average life expectancy of 78 years? The bar graph shows the average number of years you will devote to each of your most time-consuming activities. Exercises \(21-22\) are based on the data displayed by the graph. (GRAPH CANNOT COPY) According to the American Bureau of Labor Statistics, you will devote 37 years to sleeping and watching TV. The number of years sleeping will exceed the number of years watching TV by 19. Over your lifetime, how many years will you spend on each of these activities?

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$-6+y=-17$$

Use the addition property of inequality to solve each inequality and graph the solution set on a number line. \(x-3>4\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(S=P+P r t\) for \(r\)

Solve each equation in using the multiplication property of equality. Be sure to check your proposed $$-x=23$$

Solve each equation. Be sure to check your proposed solution by substituting it for the variable in the original equation. $$8(y+2)=2(3 y+4)$$

According to the American Bureau of Labor Statistics, you will devote 37 years to sleeping and watching TV. The number of years sleeping will exceed the number of years watching TV by 19. Over your lifetime, how many years will you spend on each of these activities?According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eating. The number of years sleeping will exceed the number of years eating by 24 Over your lifetime, how many years will you spend on each of these activities?

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$-8+y=-29$$

Use the addition property of inequality to solve each inequality and graph the solution set on a number line. \(x+1<6\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(S=P+P r t\) for \(t\)

Solve each equation in using the multiplication property of equality. Be sure to check your proposed $$-47=-y$$

Solve each equation. Be sure to check your proposed solution by substituting it for the variable in the original equation. $$8(y+3)=3(2 y+12)$$

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$x+\frac{1}{3}=\frac{7}{3}$$

Use the addition property of inequality to solve each inequality and graph the solution set on a number line. \(x+4 \leq 10\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(A=\frac{1}{2} h(a+b)\) for \(b\)

Solve each equation in using the multiplication property of equality. Be sure to check your proposed $$-51=-y$$

Solve each equation. Be sure to check your proposed solution by substituting it for the variable in the original equation. $$3(x+1)=7(x-2)-3$$

The bar graph shows average yearly earnings in the United States for people with a college education, by final degree earned. Exercises \(23-24\) are based on the data displayed by the graph. (GRAPH CANNOT COPY) The average yearly salary of an American whose final degree is a doctorate is 39 dollars thousand less than twice that of an American whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn 126 dollars thousand. Find the average yearly salary of Americans with each of these final degrees.

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$x+\frac{7}{8}=\frac{9}{8}$$

Use the addition property of inequality to solve each inequality and graph the solution set on a number line. \(x-5 \geq 2\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(A=\frac{1}{2} h(a+b)\) for \(a\)

Solve each equation in using the multiplication property of equality. Be sure to check your proposed $$-\frac{x}{5}=-9$$

Solve each equation. Be sure to check your proposed solution by substituting it for the variable in the original equation. $$5 x-4(x+9)=2 x-3$$

In Exercises \(25-26,\) use the fact that page numbers on facing pages of a book are consecutive integers. The sum of the page numbers on the facing pages of a book is \(629 .\) What are the page numbers?

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$t+\frac{5}{6}=-\frac{7}{12}$$

Use the addition property of inequality to solve each inequality and graph the solution set on a number line. \(y-2<0\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(A x+B y=C\) for \(x\)

Solve each equation in using the multiplication property of equality. Be sure to check your proposed $$-\frac{x}{5}=-1$$

Solve each equation. Be sure to check your proposed solution by substituting it for the variable in the original equation. $$5(2 x-8)-2=5(x-3)+3$$

Use the fact that page numbers on facing pages of a book are consecutive integers. The sum of the page numbers on the facing pages of a book is \(525 .\) What are the page numbers?

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$t+\frac{2}{3}=-\frac{7}{6}$$