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Algebra I Chapter 3 Study Guide Name: ________________________________________________ 10/07/11 3.1/3.2: Solving one-step equations with addition/subtraction and multiplication/division Know definitions of the following: Additive Inverse: Additive Identity: Multiplicative Inverse: Multiplicative Identity: Examples of problems: x – 10 = -4 x + 6 = -17 2x 24 5 x 30 6 3.3: Solving two-step equations Examples of problems: Keep answers in fraction form where necessary. 3x + 10 = 31 15 – 6x = -9 2 (6x 18) 5 22 3 3 1 x6 x2 4 6 Word Problems: Define a variable, write an equation, and solve. Find three consecutive integers whose sum is 1,038. Twenty-nine is 13 added to 4 times a number. Find the number. A number is decreased by 35. Then multiplied by one-half. Then increased by 54. Then divided by 11. The result is 4. What is the number? 3.4: Angles and Triangles in Algebra Know definitions of the following: Complementary Angles: Supplementary Angles: Name triangles based on their sides: Name triangles based on their angles: Examples of Complementary and Supplementary angles: Find each for the given angle. 54 103 (x – 65) (y + 22) Word Problems: Define a variable, write an equation and solve. The measure of an angle is 43 greater than its complement. Find the measure of each angle. In an isosceles triangle, the vertex angle measures 37. What is the measure of the base angles? The angles of a triangle are given as 2x, (x – 12) and (3x + 15) 3.5: Solving equation with variables on both sides. Examples of problems: Keep answer in fraction form where necessary. 17 + 2n = 21 + 2n 2(x – 3) + 5 = 3(x – 1) 1 3(2n 5) (12n 30) 2 7 3t t 4 8 -8(4 + 9x) = 7(-2 – 11x) 4m 5 m 2 6 5 Examples of word problems: Define a variable, write an equation and solve. Three times the greatest of three consecutive even integers is twice the least increased by 38. Find all of the numbers. One half of a number increased by 16 is four less than two thirds of the number. Find the number. 3.6: Solving an equation for a given variable. Given the equation or formula, solve for the indicated variable. ex 2y 3z , solve for x by 2 c , solve for y 3 c 3 y 2bm , solve for y 4 Word Problems: write an equation and solve for the specified variable. Four times a number x increased by 15 is 22 less than three fourths of a number y. Solve for y. Questions/Comments: