1. Equations & Inequalities

Solve and check: 24 + 3 (x + 2) = 5(x − 12).

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. s = 1/2gt², for g (distance traveled by a falling object)

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.5/2x - 8/9 = 1/18 - 1/3x

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

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.1/(x - 1) + 5 = 11/(x - 1)

Solve each equation for x. 2(x-a) +b =3x+a

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 for x. ax+b=3(x-a)

Solve each equation for x. x/a-1 = ax+3

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/(2x - 2) + 1/2 = 2/(x - 1)

Solve each equation for x. a²x + 3x =2a²

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 + 2) + 2/(x - 2) = 8/(x + 2)(x - 2)

Solve: 2x(x+3)+6(x−3)=−28. (Section 5.7, Example 2)

In Exercises 61–66, find all values of x satisfying the given conditions.y1 = 5(2x - 8) - 2, y2 = 5(x - 3) + 3, and y1 = y2.

In Exercises 61–66, find all values of x satisfying the given conditions.y1 = (x - 3)/5, y2 = (x - 5)/4, and y1 - y2 = 1.