1. Equations & Inequalities

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)^2/3 = 16

Solve and check each linear equation. 2(x - 1) + 3 = x - 3(x + 1)

Solve each problem. Suppose r varies directly as the square of m, and inversely as s. If r=12 when m=6 and s=4, find r when m=6 and s=20.

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. 2/(x - 2) = x/(x - 2) - 2

Solve each problem. If y varies directly as x, and y=20 when x=4, find y when x = -6.

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

Exercises 73–75 will help you prepare for the material covered in the next section. Simplify: √18 - √8

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 = 2x/3 + 1

In Exercises 61–66, find all values of x satisfying the given conditions. $y_1 = \(\frac{x - 3}{5}\), \(\quad\) y_2 = \(\frac{x - 5}{4}\), \(\quad\) \(\text{and}\) \(\quad\) y_1 - y_2 = 1$

Find b such that (4x - b)/(x - 5) = 3 has a solution set given by {Ø}.

Solve and check each linear equation. x - 5(x + 3) = 13

Retaining the Concepts. Solve and determine whether 8(x - 3) + 4 = 8x - 21 is an identity, a conditional equation, or an inconsistent equation.

Solve each equation. 3/(x²+x-2) - 1/(x²-1) = 7/(2x²+6x+4)

What is an inconsistent equation? Give an example.