Chapter 3

Explain the difference between a rate and a ratio.

Give an example of a formula. State what real-life quantity each variable represents.

Is the equation \(-2(4-x)=2 x-8\) an identity? Explain why or why not.

What special notation do you need to use when you are giving an approximate answer?

Two equations that have the same solutions are called \(\underline{?}\) equations.

Name two pairs of inverse operations.

Which model would you use to change 14 yards to feet? Explain. A. 14 yards \(\cdot \frac{1 \text { yard }}{3 \text { feet }}\) B. 14 yards \(\cdot \frac{3 \text { feet }}{1 \text { yard }}\)

Tell whether the formula shows correctly the relationships among perimeter, length, and width of a rectangle. $$P=2 l+2 w$$

Decide if the statement is true or false . The solution of \(x=2 x\) is zero.

Describe six ways to transform an equation into an equivalent equation.

You took a survey of your class and found that 18 out of the 31 students have a pet at home. Explain how you can use your results to make a prediction for the 1746 students in your school.

Solve \(9(9-x)=4 x-10 .\) Explain what you are doing at each step.

In Exercises 3 and \(4,\) school buses that hold 68 people will be used to transport 377 students and 65 teachers. Write and solve an equation to find the number of buses needed.

solve the equation. Show how to check your solution. $$4 x+3=11$$

Tell whether the formula shows correctly the relationships among perimeter, length, and width of a rectangle. $$P=2(l+w)$$

Solve the equation if possible. Does the equation have one solution, is it an identity, or does it have no solution? $$ 2 x+3=7 x $$

Solve the equation. $$r+3=2$$

solve the equation. Show how to check your solution. $$\frac{1}{2} x-9=11$$

Solve the equation. $$6 x=18$$

Convert the currency using the given exchange rate. Convert 200 euros to United States dollars. (1 euro is 1.066 dollar.)

Tell whether the formula shows correctly the relationships among perimeter, length, and width of a rectangle. $$l=\frac{P-2 w}{2}$$

Solve the equation if possible. Does the equation have one solution, is it an identity, or does it have no solution? $$ 12-2 a=-5 a-9 $$

Round to the nearest tenth. $$ 23.4459 $$

Solve the equation. $$9=x-4$$

solve the equation. Show how to check your solution. $$3 x-x+15=41$$

Solve the equation. $$\frac{y}{4}=8$$

Solve the equation if possible. Does the equation have one solution, is it an identity, or does it have no solution? $$ x-2 x+3=3-x $$

Round to the nearest tenth. $$ 108.2135 $$

Solve the equation. $$7+c=-10$$

solve the equation. Show how to check your solution. $$5(x-7)=90$$

Solve the equation. $$\frac{r}{-5}=20$$

Write and solve an equation to find the unknown number. $$45 \% \text { of } 280=?$$

Use this U.S. postal regulation: a rectangular package can have a combined length and girth of 108 inches. Suppose a package that is 36 inches long and as wide as it is high just meets the regulation. CHOOSING A MODEL Choose the equation you would use to find the width of the package. Then find its width. A. \(x+36=108\) B. \(2 x+36=108 \quad\) C. \(4 x+36=108\)

Solve the equation if possible. Does the equation have one solution, is it an identity, or does it have no solution? $$ 5 x+24=5(x-5) $$

Round to the nearest tenth. $$ -13.8953 $$

Solve the equation. $$-3=b-6$$

solve the equation. Show how to check your solution. $$\frac{3}{4}(x+6)=12$$

Solve the equation. $$\frac{5}{6} a=-10$$

Write and solve an equation to find the unknown number. $$7.5 \% \text { of } 340=?$$

Write a formula that describes the side length \(s\) of a square as a function of its perimeter \(P.\)

Use this U.S. postal regulation: a rectangular package can have a combined length and girth of 108 inches. Suppose a package that is 36 inches long and as wide as it is high just meets the regulation. MAKING A TABLE Make a table showing possible dimensions, girth, and combined length and girth for a "package that is 36 inches long and as wide as it is high." Which package in your table just meets the postal regulation?

Solve the equation if possible. Does the equation have one solution, is it an identity, or does it have no solution? $$ \frac{2}{3}(6 c+3)=6(c-3) $$

Round to the nearest tenth. $$ 62.9788 $$

Solve the equation. $$8-x=4$$

solve the equation. Show how to check your solution. $$6 x-4(-3 x+2)=10$$

Solve the equation. $$-7 b=-4$$

Write and solve an equation to find the unknown number. $$20 \% \text { of } \underline{?}=15$$

Rewrite the equation \(2 x+2 y=10\) so that \(y\) is a function of \(x .\)

Find the resulting unit of measure. (hours per day) \(\cdot\) (days)

Solve the equation if possible. Does the equation have one solution, is it an identity, or does it have no solution? $$ 6 y-(3 y-6)=5 y-4 $$