1. Equations & Inequalities

Solve each equation in Exercises 83–108 by the method of your choice. 1/x + 1/(x + 3) = 1/4

Solve each equation in Exercises 83–108 by the method of your choice. 2x/(x - 3) + 6/(x + 3) = - 28/(x² - 9)

Solve each equation in Exercises 83–108 by the method of your choice. 3/(x - 3) + 5/(x - 4) = (x² - 20)/(x² - 7x + 12)

Find all values of x satisfying the given conditions. y₁ = 2x² + 5x - 4, y₂ = - x² + 15x - 10, and y₁ - y₂ = 0

Solve each equation by the method of your choice. 1/(x² - 3x + 2) = 1/(x + 2) + 5/(x² - 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. $\mid x^2+2x-36\mid =12$

In Exercises 91–100, find all values of x satisfying the given conditions.$y_1 = 6 \left( \frac{2x}{x - 3} \right)^2, \quad y_2 = 5 \left( \frac{2x}{x - 3} \right), \quad \text{and} \quad y_1 \text{ exceeds } y_2 \text{ by } 6.$

In Exercises 91–100, find all values of x satisfying the given conditions. $y = x - \sqrt{x - 2} \quad \text{and} \quad y = 4$

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. $\mid x^2-6\mid =\mid 5x\mid$

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