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3x = - 6 3 3 x =- 2 Example 6: Solve for x. 6x + 3 = 4x + 5 Add –3 to each side. 6x + 3 = 4x + 5 -3 -3 6x = 4x + 2 43 44 CliffsQuickReview Algebra I Add –4x to each side. 6x = 4x + 2 - 4x - 4x 2x = 2 Divide each side by 2. 2x = 2 2 2 x=1 Literal equations Literal equations have no numbers, only symbols (letters). Example 7: Solve for Q. QP – X = Y First add X to both sides. QP - X = Y +X +X QP =Y+X Then divide both sides by P. QP Y + X P = P Q = Y +P X Operations opposite to those in the original equation were used to isolate Q.

31⁄3 × 21⁄4 = 10⁄3 × 9⁄4 = 90⁄12 = 76⁄12 = 71⁄2 or 5 3 10 Y # 9 = 15 = 7 12 Y 3 Y 4 2 1 2 Change the answer, if in improper fraction form, back to a mixed number and reduce if necessary. Remember, the rules for multiplication of signed numbers apply here as well. Dividing fractions To divide fractions, invert (turn upside down) the second fraction (the one “divided by”) and multiply. Then reduce if possible. Example 13: Divide. (a) 61 ' 15 = 61 # 51 = 65 1 3=1 (b) 19 ' 13 = 1 # Y Y 9 1 3 3 Here too the rules for division of signed numbers apply.

3 is an element of the set of 1, 2, 3. Special sets A subset is a set within a set—{2, 3} 1 {1, 2, 3}. The set of 2, 3 is a subset of the set of 1, 2, 3. The universal set is the general category set, or the set of all those elements under consideration. The empty set, or null set, is a set with no members— 4 or { }. Describing sets Rule is a method of naming a set by describing its elements. {x|x > 3, x is a whole number} {all students in the class with blue eyes} Roster is a method of naming a set by listing its members.