Chapter 2

For Problems \(51-66\), use an algebraic approach to solve each problem. Find three consecutive integers whose sum is 42 .

Solve each equation and inequality. \(|4 x+3|-2 \leq 5\)

Solve each compound inequality using the compact form. Express the solution sets in interval notation. \(-1 \leq \frac{x+2}{4} \leq 1\)

Solve each inequality and express the solution set using interval notation. \(3(x-1) \geq-(x+4)\)

For Problems \(54-63\), solve each equation and express the solutions in decimal form. Be sure to check your solutions. Use your calculator whenever it seems helpful. \(1.2 x+3.4=5.2\)

Use an algebraic approach to solve each problem. The average of the salaries of Tim, Maida, and Aaron is \(\$ 24,000\) per year. Maida earns \(\$ 10,000\) more than Tim, and Aaron's salary is \(\$ 2000\) more than twice Tim's salary. Find the salary of each person.

For Problems \(51-66\), use an algebraic approach to solve each problem. Find four consecutive integers whose sum is \(-118\).

Use an algebraic approach to solve each problem. Find four consecutive integers whose sum is \(-118\).

For Problems \(55-64\), solve each equation and inequality by inspection. \(|2 x+1|=-4\)

Solve each compound inequality using the compact form. Express the solution sets in interval notation. \(-3<2-x<3\)

Solve each inequality and express the solution set using interval notation. \(5(x-4)-6(x+2)<4\)

Solve each of Problems \(47-62\) by setting up. Juan starts walking at 4 miles per hour. An hour and a half later, Cathy starts jogging along the same route at 6 miles per hour. How long will it take Cathy to catch up with Juan?

Solve each equation and express the solutions in decimal form. Be sure to check your solutions. Use your calculator whenever it seems helpful. \(0.12 x-0.24=0.66\)

Use an algebraic approach to solve each problem. One of two supplementary angles is \(4^{\circ}\) more than onethird of the other angle. Find the measure of each of the angles.

Use an algebraic approach to solve each problem. Find three consecutive odd integers such that three times the second minus the third is 11 more than the first.

Solve each equation and inequality by inspection. \(|5 x-1|=-2\)

Solve each compound inequality using the compact form. Express the solution sets in interval notation. \(-4<3-x<4\)

Solve each inequality and express the solution set using interval notation. \(3(x+2)-4(x-1)<6\)

Solve each of Problems \(47-62\) by setting up. A car leaves a town at 60 kilometers per hour. How long will it take a second car, traveling at 75 kilometers per hour, to catch the first car if it leaves 1 hour later?

Solve each equation and express the solutions in decimal form. Be sure to check your solutions. Use your calculator whenever it seems helpful. \(0.12 x+0.14(550-x)=72.5\)

Use an algebraic approach to solve each problem. If one-half of the complement of an angle plus threefourths of the supplement of the angle equals \(110^{\circ}\), find the measure of the angle.

Use an algebraic approach to solve each problem. Find three consecutive even integers such that four times the first minus the third is six more than twice the second.

Solve each equation and inequality by inspection. \(|3 x-1|>-2\)

For Problems \(57-67\), solve each problem by setting up and solving an appropriate inequality. Suppose that Lance has \(\$ 500\) to invest. If he invests \(\$ 300\) at \(9 \%\) interest, at what rate must he invest the remaining \$200 so that the two investments yield more than \(\$ 47\) in yearly interest?

Solve each inequality and express the solution set using interval notation. \(-3(3 x+2)-2(4 x+1) \geq 0\)

Solve each of Problems \(47-62\) by setting up. Bret started on a 70-mile bicycle ride at 20 miles per hour. After a time he became a little tired and slowed down to 12 miles per hour for the rest of the trip. The entire trip of 70 miles took \(4 \frac{1}{2}\) hours. How far had Bret ridden when he reduced his speed to 12 miles per hour?

Solve each equation and express the solutions in decimal form. Be sure to check your solutions. Use your calculator whenever it seems helpful. \(0.7 n+1.4=3.92\)

Use an algebraic approach to solve each problem. If the complement of an angle is \(5^{\circ}\) less than one-sixth of its supplement, find the measure of the angle.

Use an algebraic approach to solve each problem. The difference of two numbers is 67 . The larger number is three less than six times the smaller number. Find the numbers.

Solve each problem by setting up and solving an appropriate inequality. Mona invests \(\$ 100\) at \(8 \%\) yearly interest. How much does she have to invest at \(9 \%\) so that the total yearly interest from the two investments exceeds \(\$ 26\) ?

Solve each inequality and express the solution set using interval notation. \(-4(2 x-1)-3(x+2) \geq 0\)

Solve each of Problems \(47-62\) by setting up. How many gallons of a \(12 \%\)-salt solution must be mixed with 6 gallons of a \(20 \%\)-salt solution to obtain a \(15 \%\)-salt solution?

Solve each equation and express the solutions in decimal form. Be sure to check your solutions. Use your calculator whenever it seems helpful. \(0.14 n-0.26=0.958\)

Use an algebraic approach to solve each problem. In \(\triangle A B C\), angle \(B\) is \(8^{\circ}\) less than one-half of angle \(A\) and angle \(C\) is \(28^{\circ}\) larger than angle \(A\). Find the measures of the three angles of the triangle.

Use an algebraic approach to solve each problem. The sum of two numbers is 103 . The larger number is one more than five times the smaller number. Find the numbers.

Solve each equation and inequality by inspection. \(|5 x-2|=0\)

Solve each problem by setting up and solving an appropriate inequality. The average height of the two forwards and the center of a basketball team is 6 feet and 8 inches. What must the average height of the two guards be so that the team average is at least 6 feet and 4 inches?

Solve each inequality and express the solution set using interval notation. \(-(x-3)+2(x-1)<3(x+4)\)

Solve each of Problems \(47-62\) by setting up. Suppose that you have a supply of a \(30 \%\) solution of alcohol and a \(70 \%\) solution of alcohol. How many quarts of each should be mixed to produce 20 quarts that is \(40 \%\) alcohol?

Solve each equation and express the solutions in decimal form. Be sure to check your solutions. Use your calculator whenever it seems helpful. \(0.3(d+1.8)=4.86\)

Explain why the solution set of the equation \(x+3=\) \(x+4\) is the null set.

Use an algebraic approach to solve each problem. Angelo is paid double time for each hour he works over 40 hours in a week. Last week he worked 46 hours and earned \(\$ 572\). What is his normal hourly rate?

Solve each equation and inequality by inspection. \(|3 x-1|=0\)

Solve each problem by setting up and solving an appropriate inequality. Thanh has scores of \(52,84,65\), and 74 on his first four math exams. What score must he make on the fifth exam to have an average of 70 or better for the five exams?

Solve each inequality and express the solution set using interval notation. \(3(x-1)-(x-2)>-2(x+4)\)

Solve each of Problems \(47-62\) by setting up. How many cups of grapefruit juice must be added to 40 cups of punch that is \(5 \%\) grapefruit juice to obtain a punch that is \(10 \%\) grapefruit juice?

Solve each equation and express the solutions in decimal form. Be sure to check your solutions. Use your calculator whenever it seems helpful. \(0.3(d+1.8)=4.86\)

Explain why the solution set of the equation \(\frac{x}{3}+\frac{x}{2}=\) \(\frac{5 x}{6}\) is the entire set of real numbers.

Use an algebraic approach to solve each problem. Suppose that a plumbing repair bill, not including tax, was \(\$ 130\). This included \(\$ 25\) for parts and an amount for 5 hours of labor. Find the hourly rate that was charged for labor.

Solve each problem by setting up and solving an appropriate inequality. Marsha bowled 142 and 170 in her first two games. What must she bowl in the third game to have an average of at least 160 for the three games?