Chapter 2

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?

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

State the addition property of equality and give an example.

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

A sofa regularly sells for \(\$ 840 .\) The sale price is \(\$ 714\). Find the percent decrease in the sofa's 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. $$3-x=2 x+3$$

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

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

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

A fax machine regularly sells for \(\$ 380 .\) The sale price is \(\$ 266\). Find the percent decrease in the machine's 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. $$5-x=4 x+5$$

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?

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

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?

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

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

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

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?

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

What is an angle?

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

State the multiplication property of equality and give an example.

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

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

If the measures of two angles of a triangle are known, cxplain 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.

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

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

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

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

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.

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

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

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

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.

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

Make Sense? Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I used the addition and multiplication properties of equality to solve \(3 x=20+4\)

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

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 \(y=a+b\)

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

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.

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

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. \(\frac{x}{4}-3 \geq 1\)

Make Sense? Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. When I use the addition and multiplication properties to solve \(2 x+5=17,\) I undo the operations in the opposite order in which they are performed.

Solve each equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. $$0.04(x-2)=0.02(6 x-3)-0.02$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\text { If } a x+b=0, \text { then } x=\frac{b}{a}$$