1. Equations & Inequalities

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies inversely as x. y = 12 when x = 5. Find y when x = 2.

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies jointly as x and z. y = 25 when x = 2 and z = 5. Find y when x = 8 and z = 12.

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 10x + 3 = 8x + 3

Solve each problem. Let a be directly proportional to m and n², and inversely proportional to y³. If a=9when m=4, n=9, and y=3, find a when m=6, n=2, and y=5.

Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as z and inversely as the sum of y and w.

Solve the equation. $\(\frac{5}{x}\)-\(\frac{2}{3x}\)=4+\(\frac{3}{x}\)$

Describe in words the variation shown by the given equation. $z = \(\frac{k\sqrt{x}\)}{y^2}$

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)^3/2 = 27