1. Equations & Inequalities

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.

In Exercises 61–66, find all values of x satisfying the given conditions.y1 = (2x - 1)/(x^2 + 2x - 8), y2 = 2/(x + 4), y3 = 1/(x - 2), and y1 + y2 = y3.

In Exercises 67–70, find all values of x such that y = 0.y = 2[3x - (4x - 6)] - 5(x - 6)

In Exercises 67–70, find all values of x such that y = 0.y = (x + 6)/(3x - 12) - 5/(x - 4) - 2/3

In Exercises 67–70, find all values of x such that y = 0.y = 1/(5x + 5) - 3/(x + 1) + 7/5

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation.4x + 7 = 7(x + 1) - 3x

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation.4(x + 5) = 21 + 4x

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

Exercises 73–75 will help you prepare for the material covered in the next section.Rationalize the denominator: (7 + 4√2)/(2 - 5√2).

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

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.4/(x - 2) + 3/(x + 5) = 7/(x + 5)(x - 2)