Chapter 2

Solve each equation for the indicated variable. \(-7 x-y=4\) for \(y\)

Solve each equation. If a computer costs an electronics dealer \(\$ 300\), and she sells them for \(\$ 800\), what is her rate of profit based on the selling price?

Solve each equation. \(3 x-1+\frac{2}{7}(7 x-2)=-\frac{11}{7}\)

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

Solve each equation and inequality. \(|-3 x-4| \leq 15\)

Solve each compound inequality and graph the solution sets. Express the solution sets in interval notation. \(3 x+2>17 \quad\) and \(\quad x \geq 0\)

Express each interval as an inequalit using the variable \(x\). For example, we can express the inter val \([5, \infty)\) as \(x \geq 5\). \(6 x-4 \leq 5 x-4\)

Solve each equation for the indicated variable. \(3 x-2 y=-1 \quad\) for \(y\)

Solve each equation. A textbook costs a bookstore \(\$ 45\), and the store sells it for \(\$ 60\). Find the rate of profit based on the selling price.

Solve each equation. \(2 x+5+\frac{1}{2}(6 x-1)=-\frac{1}{2}\)

Solve each equation. \(-6(x-4)-10=-12\)

Solve each equation and inequality. \(\left|\frac{x-3}{4}\right|<2\)

Solve each compound inequality and graph the solution sets. Express the solution sets in interval notation. \(5 x-2<0\) and \(3 x-1>0\)

For Problems \(41-70\), solve each inequality and express the solution set using interval notation. 2 x-1>6

Solve each equation for the indicated variable. \(3(x-2 y)=4\) for \(x\)

Solve each equation. Mitsuko's salary for next year is \(\$ 34,775\). This represents a \(7 \%\) increase over this year's salary. Find Mitsuko's present salary.

For Problems \(41-58\), use an algebraic approach to solve each problem. Find a number such that one-half of the number is 3 less than two-thirds of the number.

\(-2(3 x+5)=-3(4 x+3)\)

Solve each equation and inequality. \(\left|\frac{x+2}{3}\right|<1\)

Solve each compound inequality and graph the solution sets. Express the solution sets in interval notation. \(x+1>0 \quad\) and \(\quad 3 x-4<0\)

Solve each inequality and express the solution set using interval notation. 3 x-2<12

Solve each equation for the indicated variable. \(7(2 x+5 y)=6\) for \(y\)

Solve each equation. Don bought a used car for \(\$ 15,794\), with \(6 \%\) tax included. What was the price of the car without the tax?

Use an algebraic approach to solve each problem. One-half of a number plus three-fourths of the number is 2 more than four- thirds of the number. Find the number.

Solve each equation. \(-(2 x-1)=-5(2 x+9)\)

Solve each equation and inequality. \(\left|\frac{2 x+1}{2}\right|>1\)

Solve each compound inequality and graph the solution sets. Express the solution sets in interval notation. \(3 x+2<-1\) or \(3 x+2>1\)

Solve each inequality and express the solution set using interval notation. -5 x-2<-14

Solve each equation for the indicated variable. \(\frac{y-a}{b}=\frac{x+b}{c}\) for \(x\)

Solve each equation. Eva invested a certain amount of money at \(10 \%\) interest and \(\$ 1500\) more than that amount at \(11 \%\). Her total yearly interest was \(\$ 795\). How much did she invest at each rate?

Use an algebraic approach to solve each problem. Suppose that the width of a certain rectangle is 1 inch more than one-fourth of its length. The perimeter of the rectangle is 42 inches. Find the length and width of the rectangle.

Solve each equation. \(3(x-4)-7(x+2)=-2(x+18)\)

Solve each equation and inequality. \(\left|\frac{3 x-1}{4}\right|>3\)

Solve each compound inequality and graph the solution sets. Express the solution sets in interval notation. \(5 x-2<-2\) or \(5 x-2>2\)

Solve each inequality and express the solution set using interval notation. 5-4 x>-2

Solve each equation for the indicated variable. \(\frac{x-a}{b}=\frac{y-a}{c}\) for \(y\)

Solve each equation. A total of \(\$ 4000\) was invested, part of it at \(8 \%\) interest and the remainder at \(9 \%\). If the total yearly interest amounted to \(\$ 350\), how much was invested at each rate?

Use an algebraic approach to solve each problem. Suppose that the width of a rectangle is 3 centimeters less than two-thirds of its length. The perimeter of the rectangle is 114 centimeters. Find the length and width of the rectangle.

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

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

For Problems 45-56, solve each compound inequality using the compact form. Express the solution sets in interval notation. \(-3<2 x+1<5\)

Solve each inequality and express the solution set using interval notation. -3(2 x+1) \geq 12

Solve each equation for the indicated variable. \((y+1)(a-3)=x-2\) for \(y\)

Solve each equation. A sum of \(\$ 95,000\) is split between two investments, one paying \(6 \%\) and the other \(9 \%\). If the total yearly interest amounted to \(\$ 7290\), how much was invested at \(9 \%\) ?

Use an algebraic approach to solve each problem. Find three consecutive integers such that the sum of the first plus one-third of the second plus three-eighths of the third is 25 .

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

Solve each equation and inequality. \(|3 x-1|-1=9\)

Solve each compound inequality using the compact form. Express the solution sets in interval notation. \(-7<3 x-1<8\)

Solve each inequality and express the solution set using interval notation. -2(3 x+2) \leq 18

Solve each equation for the indicated variable. \((y-2)(a+1)=x \quad\) for \(y\)