In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 4(3x - 2) - 3x < 3(1 + 3x) - 7

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? S = P + Prt for r

Write each English sentence as an equation in two variables. Then graph the equation. The y-value is four more than twice the x-value.

Solve each equation in Exercises 41–60 by making an appropriate substitution. x^(-2) - x^(-1) - 6 = 0

Write each English sentence as an equation in two variables. Then graph the equation. The y-value is the difference between four and twice the x-value.

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 1/(x - 1) + 5 = 11/(x - 1)

Solve each equation in Exercises 47–64 by completing the square. $x^2-2x=2$

Perform the indicated operations and write the result in standard form. $\sqrt{-8} \left( \sqrt{-3} - \sqrt{-5} \right)$

In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 5(x - 2) - 3(x + 4) ≥ 2x - 20

Write each English sentence as an equation in two variables. Then graph the equation. The y-value is three decreased by the square of the x-value.

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(x + 4) - 7 = - 4/(x + 4)

Perform the indicated operations and write the result in standard form. (7-i)(2+3i)

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? S = C/(1 - r) for r

Solve each equation in Exercises 47–64 by completing the square. $x^2+4x=12$

Write each English sentence as an equation in two variables. Then graph the equation. The y-value is two more than the square of the x-value.

Solve each equation in Exercises 47–64 by completing the square. $x^2-6x-11=0$

In Exercises 51–58, solve each compound inequality. 6 < x + 3 < 8

In Exercises 37–52, perform the indicated operations and write the result in standard form. (3√-5)(- 4√-12)

Write each English sentence as an equation in two variables. Then graph the equation. y = 5 (Let x = -3, - 2, - 1, 0, 1, 2, and 3.)

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? A = 2lw + 2lh + 2wh for h

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 2/(x - 2) = x/(x - 2) - 2

Solve each equation in Exercises 41–60 by making an appropriate substitution. $x^{\frac{2}{5}}+x^{\frac{1}{5}}-6=0$

In Exercises 48–57, perform the indicated operations and write the result in standard form. 6/(5+i)

Solve each equation in Exercises 47–64 by completing the square. $x^2+4x+1=0$

In Exercises 53–60, write each power of i as as i, - 1, - i, or 1. i³¹

In Exercises 51–58, solve each compound inequality. - 3 ≤ x - 2 < 1

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(2x - 2) + 1/2 = 2/(x - 1)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? 1/R = 1/R₁ + 1/R₂ for R₁

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(x + 2) + 2/(x - 2) = 8/(x + 2)(x - 2)

Solve each equation in Exercises 47–64 by completing the square. $x^2-5x+6=0$