Chapter 2

Did you have some difficulties solving some of the problems that were assigned in this Exercise Set? Discuss what you did if this happened to you. Did your course of action enhance your ability to solve algebraic word problems?

Use the five-step problem-solving strategy to find the measure of the angle described. The measure of the angle's supplement is \(10^{\circ}\) more than three times that of its complement.

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$7 y+4=6 y-9$$

Use the multiplication property of inequality to solve each inequality and graph the solution set on a number line. \(-3 x \geq 15\)

Solve each equation in using both the addition and multiplication properties of equality. Check proposed solutions. $$6 z-5=z+5$$

Solve each equation and check your proposed solution in Exercises. $$0.92 y+2=y-0.4$$

Write an original word problem that can be solved using a linear equation. Then solve the problem.

Use the five-step problem-solving strategy to find the measure of the angle described. The measure of the angle's supplement is \(52^{\circ}\) more than twice that of its complement.

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$4 r-3=5+3 r$$

Use the multiplication property of inequality to solve each inequality and graph the solution set on a number line. \(-7 x \leq 21\)

Solve each equation in using both the addition and multiplication properties of equality. Check proposed solutions. $$6 z-3=z+2$$

Solve each equation and check your proposed solution in Exercises. $$0.15 y-0.1=2.5 y-1.04$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Rather than struggling with the assigned word problems, I'll ask my instructor to solve them all in class and then study the solutions.

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$12-6 x=18-7 x$$

Use the multiplication property of inequality to solve each inequality and graph the solution set on a number line. \(-16 x>-4\)

Solve each equation in using both the addition and multiplication properties of equality. Check proposed solutions. $$6 x+14=2 x-2$$

The average, or mean, \(A,\) of three exam grades, \(x, y,\) and \(z,\) is given by the formula $$A=\frac{x+y+z}{3}$$ a. Solve the formula for \(z\). b. Use the formula in part (a) to solve this problem. On your first two exams, your grades are \(86 \%\) and \(88 \%\) : \(x=86\) and \(y=88 .\) What must you get on the third exam to have an average of \(90 \% ?\)

Solve each equation and check your proposed solution in Exercises. $$0.3 x-4=0.1(x+10)$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. By reasoning through word problems, I can increase my problem-solving skills in general.

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$20-7 s=26-8 s$$

Use the multiplication property of inequality to solve each inequality and graph the solution set on a number line. \(-20 x>-140\)

Solve each equation in using both the addition and multiplication properties of equality. Check proposed solutions. $$9 x+2=6 x-4$$

The average, or mean, \(A\), of four exam grades, \(x, y, z,\) and \(w,\) is given by the formula $$A=\frac{x+y+z+w}{4}$$ a. Solve the formula for \(w\) b. Use the formula in part (a) to solve this problem. On your first three exams, your grades are \(76 \%, 78 \%,\) and \(79 \%: x=76, y=78,\) and \(z=79 .\) What must you get on the fourth exam to have an average of \(80 \% ?\)

Solve each equation and check your proposed solution in Exercises. $$0.1(x+80)=14-0.2 x$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I find the hardest part in solving a word problem is writing the equation that models the verbal conditions.

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$4 x+2=3(x-6)+8$$

Use the multiplication property of inequality to solve each inequality and graph the solution set on a number line. \(-4 y \leq \frac{1}{2}\)

Solve each equation in using both the addition and multiplication properties of equality. Check proposed solutions. $$ y-1=5-2 y$$

If you are traveling in your car at an average rate of \(r\) miles per hour for \(t\) hours, then the distance, \(d,\) in miles, that you travel is described by the formula \(d=r t\) : distance equals rate times time. a. Solve the formula for \(t\) b. Use the formula in part (a) to find the time that you travel if you cover a distance of 100 miles at an average rate of 40 miles per hour.

Solve each equation and check your proposed solution in Exercises. $$0.4(2 z+6)+0.1=0.5(2 z-3)$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I made a mistake when I used \(x\) and \(x+2\) to represent two consecutive odd integers, because 2 is even.

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$7 x+3=6(x-1)+9$$

Use the multiplication property of inequality to solve each inequality and graph the solution set on a number line. \(-2 y \leq \frac{1}{2}\)

Solve each equation in using both the addition and multiplication properties of equality. Check proposed solutions. $$-3 y-2=-5-4 y$$

The formula \(F=\frac{9}{5} C+32\) expresses the relationship between Celsius temperature, \(C,\) and Fahrenheit temperature, \(F\). a. Solve the formula for \(C\). b. Use the formula from part (a) to find the equivalent Celsius temperature for a Fahrenheit temperature of \(59^{\circ}\).

Solve each equation and check your proposed solution in Exercises. $$1.4(z-5)-0.2=0.5(6 z-8)$$

Use the multiplication property of inequality to solve each inequality and graph the solution set on a number line. \(-x<4\)

Solve each equation and check your proposed solution in Exercises. $$0.01(x+4)-0.04=0.01(5 x+4)$$

Use the multiplication property of inequality to solve each inequality and graph the solution set on a number line. \(-x>-3\)

Solve each equation and check your proposed solution in Exercises. $$0.02(x-2)=0.06-0.01(x+1)$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If the length of a rectangle is 6 inches more than its width, and its perimeter is 24 inches, the distributive property must be used to solve the equation that determines the length.

Use the formulas for perimeter and area in Table 2.3 on page 169 to solve. Taxpayers with an office in their home may deduct a percentage of their home- related expenses. This percentage is based on the ratio of the office's area to the area of the home. A taxpayer with a 2200 -square-foot home maintains a 20 -foot by 16 -foot office. If the yearly electricity bills for the home come to \(\$ 4800,\) how much of this is deductible?

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. \(2 x-3>7\)

The equations in contain small geometric figures that represent nonzero real numbers. Use the multiplication property of equality to isolate \(x\) on one side of the equation and the geometric figures on the other side. $$\Delta=-x$$

Solve each equation and check your proposed solution in Exercises. $$0.6(x+300)=0.65 x-205$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. On a number line, consecutive integers do not have any other integers between them.

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. \(3 x+2 \leq 14\)

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

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?

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