Chapter 2

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 12 is subtracted from a number, the result is \(-2 .\) Find the number.

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

The rate for a particular international telephone call is 0.55 dollars for the first minute and 0.40 dollars for each additional minute. Determine the length of a call that costs 6.95 dollars .

Use the formulas for the area and the circumference of a circle in Table 2.4 on page 170 to solve. Unless otherwise indicated, round all circumference and area calculations to the nearest whole number. 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 23 is subtracted from a number, the result is \(-8 .\) Find the number.

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

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.

In 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 \(-9,\) the result is \(5 .\) Find the number.

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

Solve each 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. The difference between 3 and \(\frac{2}{7}\) of a number is \(\frac{5}{4}\) of that number. Find the number.

In 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 each 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: \(\frac{4}{5} x=-16\) (Section 2.2, Example 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 $$C+M=S$$ Use the formula. 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 both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. \(-2 x-3<3\)

In 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 much was the tip?

Solve each 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: \(6(y-1)+7=9 y-y+1\) (Section \(2.3,\) Example 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 $$C+M=S$$ Use the formula. The selling price of a television is \(\$ 650 .\) If the cost to the retailer for the television is \(\$ 520,\) find the markup.

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

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

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

In 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 \(-6\)

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?

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

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 \(b=12\)

Use the formulas for volume in Table 2.5 on page 171 to solve. When necessary, round all volume calculations to the nearest whole number. A building contractor is to dig a foundation 4 yards long. 3 yards wide, and 2 yards decp 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 haulcd away?

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

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

Will help you prepare for the material covered in the next section. Evaluate \(A=\frac{1}{2} h(a+b)\) for \(a=10, b=16,\) and \(h=7\)

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?

An exercise machine with an original price of \(\$ 860\) is on sale at \(12 \%\) off. a. What is the discount amount? b. What is the exercise machine's sale price?

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

Will help you prepare for the material covered in the next section. Solve: \(\quad x=4(90-x)-40\)

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. \(6 x-2 \geq 4 x+6\)

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 3 miles away from the lightning flash, how long will it take the sound of thunder to reach you?