Chapter 2

Solve each equation. If \(\$ 1500\) is invested at \(6 \%\) interest, how much money must be invested at \(9 \%\) so that the total return for both investments is \(\$ 301.50\) ?

Use an algebraic approach to solve each problem. Lou is paid \(1 \frac{1}{2}\) times his normal hourly rate for each hour he works over 40 hours in a week. Last week he worked 44 hours and earned \(\$ 276\). What is his normal hourly rate?

Solve each equation. \(-3(4 n+2)+2(n-6)=-2(n+1)\)

Solve each equation and inequality. \(|x+2|-6=-2\)

Solve each compound inequality using the compact form. Express the solution sets in interval notation. \(-17 \leq 3 x-2 \leq 10\)

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

Solve each of Problems \(47-62\) by setting up and solving an appropriate algebraic equation. Suppose that the length of a certain rectangle is 2 meters less than four times its width. The perimeter of the rectangle is 56 meters. Find the length and width of the rectangle.

Solve each equation. Suppose that Javier has a handful of coins, consisting of pennies, nickels, and dimes, worth \(\$ 2.63\). The number of nickels is 1 less than twice the number of pennies, and the number of dimes is 3 more than the number of nickels. How many coins of each kind does he have?

Use an algebraic approach to solve each problem. A board 20 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board.

Solve each equation. \(3(2 a-1)-2(5 a+1)=4(3 a+4)\)

Solve each equation and inequality. \(|x-3|-4=-1\)

Solve each compound inequality using the compact form. Express the solution sets in interval notation. \(-25 \leq 4 x+3 \leq 19\)

Solve each inequality and express the solution set using interval notation. 3(4 x-3) \leq-11

Solve each of Problems \(47-62\) by setting up. The perimeter of a triangle is 42 inches. The second side is 1 inch more than twice the first side, and the third side is 1 inch less than three times the first side. Find the lengths of the three sides of the triangle.

Solve each equation. Sarah has a collection of nickels, dimes, and quarters worth \(\$ 15.75\). She has 10 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she have?

Use an algebraic approach to solve each problem. Jody has a collection of 116 coins consisting of dimes, quarters, and silver dollars. The number of quarters is 5 less than three-fourths of the number of dimes. The number of silver dollars is 7 more than five-eighths of the number of dimes. How many coins of each kind are in her collection?

Solve each equation. \(4(2 a+3)-3(4 a-2)=5(4 a-7)\)

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

Solve each compound inequality using the compact form. Express the solution sets in interval notation. \(<4 x+3<9\)

Solve each inequality and express the solution set using interval notation. \(6 x-2>4 x-14\)

Solve each of Problems \(47-62\) by setting up. How long will it take \(\$ 500\) to double itself at \(9 \%\) simple interest?

Solve each equation. A collection of 70 coins consisting of dimes, quarters, and half-dollars has a value of \(\$ 17.75\). There are three times as many quarters as dimes. Find the number of each kind of coin.

Use an algebraic approach to solve each problem. The sum of the present ages of Angie and her mother is 64 years. In eight years Angie will be three-fifths as old as her mother at that time. Find the present ages of Angie and her mother.

Solve each equation. \(-2(n-4)-(3 n-1)=-2+(2 n-1)\)

Solve each equation and inequality. \(|5 x+1|+4=4\)

Solve each compound inequality using the compact form. Express the solution sets in interval notation. \(0<2 x+5<12\)

Solve each inequality and express the solution set using interval notation. \(9 x+5<6 x-10\)

Solve each of Problems \(47-62\) by setting up. How long will it take \(\$ 700\) to triple itself at \(10 \%\) simple interest?

Solve each equation. Abby has 37 coins, consisting only of dimes and quarters, worth \(\$ 7.45\). How many dimes and how many quarters does she have?

Use an algebraic approach to solve each problem. Annilee's present age is two-thirds of Jessie's present age. In 12 years the sum of their ages will be 54 years. Find their present ages.

Solve each equation. \(-(2 n-1)+6(n+3)=-4-(7 n-11)\)

Solve each equation and inequality. \(|x+7|-3 \geq 4\)

Solve each compound inequality using the compact form. Express the solution sets in interval notation. \(-6<4 x-5<6\)

Solve each inequality and express the solution set using interval notation. \(2 x-7<6 x+13\)

Solve each of Problems \(47-62\) by setting up. How long will it take \(P\) dollars to double itself at \(9 \%\) simple interest?

Use an algebraic approach to solve each problem. Sydney's present age is one-half of Marcus's present age. In 12 years, Sydney's age will be five-eighths of Marcus's age. Find their present ages.

For Problems \(51-66\), use an algebraic approach to solve each problem. If 15 is subtracted from three times a certain number, the result is 27 . Find the number.

Solve each equation and inequality. \(|x-2|+4 \geq 10\)

Solve each compound inequality using the compact form. Express the solution sets in interval notation. \(-2<3 x+4<2\)

Solve each inequality and express the solution set using interval notation. \(2 x-3>7 x+22\)

Solve each of Problems \(47-62\) by setting up. How long will it take \(P\) dollars to triple itself at \(10 \%\) simple interest?

Is a \(10 \%\) discount followed by a \(30 \%\) discount the same as a \(30 \%\) discount followed by a \(10 \%\) discount? Justify your answer.

Use an algebraic approach to solve each problem. The sum of the present ages of Ian and his brother is 45 . In 5 years, Ian's age will be five-sixths of his brother's age. Find their present ages.

For Problems \(51-66\), use an algebraic approach to solve each problem. If 1 is subtracted from seven times a certain number, the result is the same as if 31 is added to three times the number. Find the number.

Solve each equation and inequality. \(|2 x-1|+1 \leq 6\)

Solve each compound inequality using the compact form. Express the solution sets in interval notation. \(-4 \leq \frac{x-1}{3} \leq 4\)

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

Solve each of Problems \(47-62\) by setting up. Two airplanes leave Chicago at the same time and fly in opposite directions. If one travels at 450 miles per hour and the other at 550 miles per hour, how long will it take for them to be 4000 miles apart?

What is wrong with the following solution and how should it be done? $$ \begin{aligned} 1.2 x+2 &=3.8 \\ 10(1.2 x)+2 &=10(3.8) \\ 12 x+2 &=38 \\ 12 x &=36 \\ x &=3 \end{aligned} $$

Use an algebraic approach to solve each problem. Aura took three biology exams and has an average score of 88 . Her second exam score was 10 points better than her first, and her third exam score was 4 points better than her second exam. What were her three exam scores?