Chapter 2

Across the United States, people generate approximately 55 billion pounds of trash in the form of plastic each year. (That's approximately 180 pounds per person per year.) How many billions of pounds of trash do we throw away each year?

Solve equation and check your proposed solution in. \(0.05(7 x+36)=0.4 x+1.2\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. An HMO pamphlet contains the following recommended weight for women: "Give yourself 100 pounds for the first \(-5\) feet plus 5 pounds for every inch over 5 feet tall." Using this description, which height corresponds to an ideal weight of 135 pounds?

Which one of the following is a better buy: a large pizza with a 14 -inch diameter for \(\$ 12.00\) or a medium pizza with a 7 -inch diameter for \(\$ 5.00 ?\)

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$3 x+3<18$$

Use the given information to write an equation. Let \(x\) represent the number described in each exercise. Then solve the equation and find the number. If a number is multiplied by \(6,\) the result is \(10 .\) Find the number.

Solve equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. \(3 x-7=3(x+1)\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The rate for a particular international telephone call is \(\$ 0.55\) for the first minute and \(\$ 0.40\) for each additional minute. Determine the length of a call that costs \(\$ 6.95\)

Which one of the following is a better buy: a large pizza with a 16 -inch diameter for \(\$ 12.00\) or two small pizzas, each with a 10 -inch diameter, for \(\$ 12.00 ?\)

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$8 x-4>12$$

Use the given information to write an equation. Let \(x\) represent the number described in each exercise. Then solve the equation and find the number. If a number is multiplied by \(-6,\) the result is \(20 .\) Find the number.

Solve equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. \(2(x-5)=2 x+10\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. In a film, the actor Charles Coburn played an elderly "uncle" character criticized for marrying a woman when he is 3 times her age. He wittily replies, "Ah, but in 20 years time I shall only be twice her age." How old is the "uncle" and the woman?

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$3-7 x \leq 17$$

Use the given information to write an equation. Let \(x\) represent the number described in each exercise. Then solve the equation and find the number. The difference between \(\frac{2}{5}\) of a number and 8 is \(\frac{7}{5}\) of that number. Find the number.

A charity has raised \(\$ 7500\), with a goal of raising \(\$ 60,000\). What percent of the goal has been raised?

Solve equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. \(2(x+4)=4 x+5-2 x+3\)

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$5-3 x \geq 20$$

Use the given information to write an equation. Let \(x\) represent the number described in each exercise. Then solve the equation and find the number. If a number is divided by \(-7,\) the result is 8. Find the number.

A charity has raised \(\$ 225,000,\) with a goal of raising \(\$ 500,000 .\) What percent of the goal has been raised?

Solve equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. \(3(x-1)=8 x+6-5 x-9\)

Solve and check: \(\frac{4}{5} x=-16\)

A glass window is to be placed in a house. The window consists of a rectangle, 6 feet high by 3 feet wide, with a semicircle at the top. Approximately how many feet of stripping, to the nearest tenth of a foot, will be needed to frame the window?

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$-2 x-3<3$$

Formulas frequently appear in the business world. For example, the cost, \(C,\) of an item (the price paid by a retailer) plus the markup, \(M,\) on that item (the retailer's profit) equals the selling price, \(S,\) of the item. The formula is $$C+M=S$$ The selling price of a computer is \(\$ 1850 .\) If the markup on the computer is \(\$ 150,\) find the cost to the retailer for the computer.

Use the given information to write an equation. Let \(x\) represent the number described in each exercise. Then solve the equation and find the number. Eight subtracted from the product of 4 and a number is 56

A restaurant bill came to \(\$ 60 .\) If \(15 \%\) of this amount was left as a tip. how mush was the tip?

Solve equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. \(7+2(3 x-5)=8-3(2 x+1)\)

Solve and check: \(6(y-1)+7=9 y-y+1\)

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$-3 x+14<5$$

Formulas frequently appear in the business world. For example, the cost, \(C,\) of an item (the price paid by a retailer) plus the markup, \(M,\) on that item (the retailer's profit) equals the selling price, \(S,\) of the item. The formula is $$C+M=S$$ The selling price of a television is \(\$ 650 .\) If the cost to the retailer for the television is \(\$ 520,\) find the markup.

Use the given information to write an equation. Let \(x\) represent the number described in each exercise. Then solve the equation and find the number. Ten subtracted from the product of 3 and a number is 23 .

If income tax is \(\$ 3502\) plus \(28 \%\) of taxable income over \(\$ 23,000,\) how much is the income tax on a taxable income of \(\$ 35.000 ?\)

Solve equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. \(2+3(2 x-7)=9-4(3 x+1)\)

A water reservoir is shaped like a rectangular solid with a base that is 50 yards by 30 yards, and a vertical height of 20 yards. At the start of a three- month period of no rain, the reservoir was completely full. At the end of this period, the height of the water was down to 6 yards. How much water was used in the three-month period?

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$5-x \leq 1$$

Use the given information to write an equation. Let \(x\) represent the number described in each exercise. Then solve the equation and find the number. Negative three times a number, increased by \(15,\) is \(-6\)

Solve equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. \(4 x+1-5 x=5-(x+4)\)

Suppose that the local sales tax rate is \(6 \%\) and you buy a car for \(\$ 16,800\) a. How much tax is due? b. What is the car's total cost?

Will help you prepare for the material covered in the next section. Use \(A=\frac{1}{2} b h\) to find \(h\) if \(A=30\) and \(b=12\)

A building contractor is to dig a foundation 4 yards long, 3 yards wide, and 2 yards deep for a toll booth's foundation. The contractor pays \(\$ 10\) per load for trucks to remove the dirt. Each truck holds 6 cubic yards. What is the cost to the contractor to have all the dirt hauled away?

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$3-x \geq-3$$

Use the given information to write an equation. Let \(x\) represent the number described in each exercise. Then solve the equation and find the number. Negative five times a number, increased by \(11,\) is \(-29\)

Suppose that the local sales tax rate is \(7 \%\) and you buy a graphing calculator for \(\$ 96\) a. How much tax is due? b. What is the calculator's total cost?

Solve equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. \(5 x-5=3 x-7+2(x+1)\)

Evaluate \(A=\frac{1}{2} h(a+b)\) for \(a=10, b=16,\) and \(h=7\)

Two cylindrical cans of soup sell for the same price. One can has a diameter of 6 inches and a height of 5 inches. The other has a diameter of 5 inches and a height of 6 inches. Which can contains more soup and, therefore, is the better buy?

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$2 x-5>-x+6$$

The formula $$ M=\frac{n}{5} $$ models your distance, \(M,\) in miles, from a lightning strike in a thunderstorm if it takes \(n\) seconds to hear thunder after seeing the lightning. Use this formula to solve. If you are 2 miles away from the lightning flash, how long will it take the sound of thunder to reach you?

Solve equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. \(4(x+2)+1=7 x-3(x-2)\)