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SIMPLIFYING expressions on either side of an equation. Linear Equations A linear equation is one which is in the form ax ϩ b ϭ 0 or can be transformed into an equivalent equation in this form. If a 2 0, a linear equation has exactly one solution. If a ϭ 0 the equation has no solutions unless b ϭ 0, in which case the equation is an identity. An equation which is not linear is called nonlinear. 3 is {–3}. 2x ϩ 6 ϭ 0 is an example of a linear equation in one variable. It has one solution, –3. 4 x2 ϭ 16 is an example of a nonlinear equation in one variable.

Ans. 5, 2i, Ϫ2i pf pϪf Ans. I ϭ ϪRC Ϯ 2R2C2 Ϫ 4LC 2LC Ans. 33. Solve for y in terms of x: (a) 3x Ϫ 5y ϭ 8; (b) x2 Ϫ 2xy ϩ y2 ϭ 4; (c) x Ϫ y ϭ 5; (d) x ϭ 2y2 Ϫ 2y Ans. 34. A rectangle has perimeter 44 cm. Find its dimensions if its length is 5 cm less than twice its width. Ans. 35. 19) if the two people start walking at the same time, but the second person walks north. Ans. m. 36. 50 per pound. How much of each type of coffee should be used? Ans. 00-per-pound coffee. 37. A container is filled with 8 centiliters of a 30% acid solution.

The inequality holds when the expression under consideration is positive; 3 hence the solution set is (Ϫ ` , Ϫ5) < 5Ϫ2 6 < [2, ` ). 12. For what values of x does the expression 29 Ϫ x2 represent a real number? The expression represents a real number when the quantity 9 Ϫ x2 is nonnegative. Solve the inequality statement 9 Ϫ x2 Ն 0, or (3 Ϫ x)(3 ϩ x) Ն 0, by drawing a number line showing the critical points 3 and Ϫ3 (Fig. 6-9). Figure 6-9 The critical points divide the real number line into the intervals (Ϫ ` , Ϫ3), (Ϫ3, 3), and (3, ` ).

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