1. Equations & Inequalities

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

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

Solve each equation in Exercises 15–34 by the square root property. (x + 2)² = 25

Solve each equation. ∜(x²+2x)= ∜3

Solve each equation. (x-2)^2/3 = x^1/3

Solve each equation. √(2x-5)=2+√(x-2)

Solve each equation. 2 - 5/x = 3/x²

Solve each equation. 3x^3/4 = x^1/2

Solve each equation. √(3x+7) = 3x+5

Solve each equation. √(4x+13) = 2x-1

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation. $x^2-4x-5=0$

Use the method described in Exercises 83–86, if applicable, and properties of absolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 can be solved by inspection.) | x² - 9 | = x + 3

Solve each equation. √(4x+1)-√(x-1)=2

Solve each equation. x^-2/3+x^-1/3-6=0

Match each equation in Column I with the correct first step for solving it in Column II. (x+5)^2/3 - (x+5)^1/3 - 6 = 0