Chapter 2

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?

$$\text { Solve: } x=4(90-x)-40$$

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?

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

A dictionary that normally sells for \(\$ 16.50\) is on sale at \(40 \%\) off. a. What is the discount amount? b. What is the dictionary's sale price?

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$2 y-5<5 y-11$$

State the addition property of equality and give an example.

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

A sofa regularly sells for \(\$ 840 .\) The sale price is \(\$ 714 .\) Find the percent decrease in the sofa's price.

Using words only, describe how to find the area of a Triangle.

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$4 y-7>9 y-2$$

Explain why \(x+2=9\) and \(x+2=-6\) are not equivalent equations.

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

A fax machine regularly sells for \(\$ 380 .\) The sale price is \(\$ 266\) Find the percent decrease in the machine's price.

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$3(2 y-1)<9$$

Describe the difference between the following problems: How much fencing is needed to enclose a garden? How much fertilizer is needed for the garden?

What is the difference between solving an equation such as $$ 5 y+3-4 y-8=6+9 $$ and simplifying an algebraic expression such as $$ 5 y+3-4 y-8 ? $$ If there is a difference, which topic should be taught first? Why?

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

Suppose that you put \(\$ 10,000\) in a rather risky investment recommended by your financial advisor. During the first year, your investment decreases by \(30 \%\) of its original value. During the second year, your investment increases by \(40 \%\) of its first-year value. Your advisor tells you that there must have been a \(10 \%\) overall increase of your original \(\$ 10,000\) investment. Is your financial advisor using percentages properly? If not, what is the actual percent gain or loss on your original \(\$ 10,000\) investment?

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$4(2 y-1)>12$$

Describe how volume is measured. Explain why linear or square units cannot be used.

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

The price of a color printer is reduced by \(30 \%\) of its original price. When it still does not sell, its price is reduced by \(20 \%\) of the reduced price. The salesperson informs you that there has been a total reduction of \(50 \% .\) Is the salesperson using percentages properly? If not, what is the actual percent reduction from the original price?

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$3(x+1)-5<2 x+1$$

What is an angle?

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. The book is teaching me totally different things than my instructor: The book adds the number to both sides beside the equation, but my instructor adds the number underneath.

State the multiplication property of equality and give an example.

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

Explain what it means to solve a formula for a variable.

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$4(x+1)+2 \geq 3 x+6$$

If the measures of two angles of a triangle are known, explain how to find the measure of the third angle.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. There are times that I prefer to check an equation's solution in my head and not show the check.

Explain how to solve the equation \(-x=-50\)

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

What does the percent formula, \(A=P B,\) describe? Give an example of how the formula is used.

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$8 x+3>3(2 x+1)-x+5$$

Can a triangle contain two \(90^{\circ}\) angles? Explain your answer.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Solving an equation reminds me of keeping a barbell balanced: If I add weight to or subtract weight from one side of the bar, I must do the same thing to the other side.

Explain how to solve the equation \(2 x+8=5 x-3\)

Solve equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. \(\frac{2}{3} x=2-\frac{5}{6} x\)

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$7-2(x-4)<5(1-2 x)$$

What are complementary angles? Describe how to find the measure of an angle's complement.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I used a linear equation to explore data points lying on the same line.

Solve equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. \(\frac{2}{3} x=\frac{1}{4} x-8\)

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$\frac{x}{3}-2 \geq 1$$

What are supplementary angles? Describe how to find the measure of an angle's supplement.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If \(y-a=-b,\) then \(y=a+b\)

Solve equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. \(0.06(x+5)=0.03(2 x+7)+0.09\)

Make Sense? In Exercises \(75-78,\) determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I have \(\$ 100\) and my restaurant bill comes to \(\$ 80,\) which is not enough to leave a \(20 \%\) tip.