1. Equations & Inequalities

Solve each equation in Exercises 83–108 by the method of your choice.2x/(x - 3) + 6/(x + 3) = - 28/(x^2 - 9)

Solve each equation in Exercises 83–108 by the method of your choice.3/(x - 3) + 5/(x - 4) = (x^2 - 20)/(x^2 - 7x + 12)

In Exercises 115–122, find all values of x satisfying the given conditions.y1 = 2x^2 + 5x - 4, y2 = - x^2 + 15x - 10, and y1 - y2 = 0

In Exercises 127–130, solve each equation by the method of your choice.1/(x^2 - 3x + 2) = 1/(x + 2) + 5/(x^2 - 4)

Write a quadratic equation in general form whose solution set is {- 3, 5}.

Solve: √(6x - 2) = √(2x + 3) - √(4x - 1).

If a number is decreased by 3, the principal square root of this difference is 5 less than the number. Find the number(s).

If 5 times a number is decreased by 4, the principal square root of this difference is 2 less than the number. Find the number(s).

In Exercises 101–106, solve each equation.x(x + 1)^3 - 42(x + 1)^2 = 0

In Exercises 101–106, solve each equation.|x^2 + 2x - 36| = 12

In Exercises 91–100, find all values of x satisfying the given conditions.y1 = 6(2x/(x - 3))^2, y2 = 5(2x/(x - 3)), and y1 exceeds y2 by 6

In Exercises 91–100, find all values of x satisfying the given conditions.y = x - √(x - 2) and y = 4

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars:If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84.|x^2 - 6| = |5x|

Solve each radical equation in Exercises 11–30. Check all proposed solutions.√(2x + 3) + √(x - 2) = 2

Solve each equation in Exercises 41–60 by making an appropriate substitution.9x^4 = 25x^2 - 16