1. Equations & Inequalities

Solve each equation. 10/(4x-4) = 1 /(1-x)

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

Solve each equation. |3/ (2x - 3) | = 4

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies jointly as a and b and inversely as the square root of c. y = 12 when a = 3, b = 2, and c = 25. Find y when a = 5, b = 3 and c = 9.

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. (x + 3)/6 = 3/8 + (x - 5)/4

Solve each equation. See Example 1. (2x+5)/2 - 3x/(x-2) = x

Evaluate x² - (xy - y) for x satisfying 3(x + 3)/5 = 2x + 6 and y satisfying - 2y - 10 = 5y + 18.

Match each statement with its corresponding graph in choices A–D. In each case, k > 0. y varies directly as x. (y=kx)

In Exercises 1–26, solve and check each linear equation. 7x + 4 = x + 16

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/5 - 1/2 = x/6

Solve each equation. (4x+3)/4 - 2x/(x+1) = x

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

Simple Interest Simple interest varies jointly as principal and time. If \$1000 invested for 2 yr earned \$70, find the amount of interest earned by \$5000 invested for 5 yr.

Circumference of a Circle The circumference of a circle varies directly as the radius. A circle with radius 7 in. has circumference 43.96 in. Find the circumference of the circle if the radius changes to 11 in.