1. Equations & Inequalities

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

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

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.) | 3x² - 14x | = 5

Solve each equation. 4x⁴+3x²-1 = 0