1. Equations & Inequalities

Solve each equation. | 5/ (x-3) | = 10

Determine the values of the variable that cannot possibly be solutions of each equation. Do not solve. 3/(x-2) + 1/(x+1) = 3/(x²-x-2)

Nuclear Bomb Detonation Suppose the effects of detonating a nuclear bomb will be felt over a distance from the point of detonation that is directly proportional to the cube root of the yield of the bomb. Suppose a 100-kiloton bomb has certain effects to a radius of 3 km from the point of detonation. Find, to the nearest tenth, the distance over which the effects would be felt for a 1500-kiloton bomb.

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z.

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

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. (x - 2)/2x + 1 = (x + 1)/x

Solve the equation. $\(\frac{2x+4}{x-1}\)=5$

In Exercises 99–106, solve each equation. [(3 + 6)² ÷ 3] × 4 = - 54 x

Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7(x-4) = x + 2

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(x + 4) - 7 = - 4/(x + 4)

Solve each equation. x/(x-1) - 1/(x+1) = 2/(x²-1)

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 4x/(x + 3) - 12/(x - 3) = (4x² + 36)/(x² - 9)

Solve each equation. 3x²/(x-2) + 2 = x/(x-1)

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 5 + (x - 2)/3 = (x + 3)/8