Download Math 95 Section 2.1 Notes Addition, Subtraction, Multiplication and

Math 95 Section 2.1 Notes Addition, Subtraction, Multiplication and Division Properties of Equality Objective: Students will utilize the addition, subtraction, multiplication, and division properties of equality to solve linear equations. Students will translate English sentences to algebraic expressions or equations. Definitions: Linear equation in one variable: Let a, b, and c be real numbers such that a is not equal to 0. A linear equation in one variable is an equation that can be written in the form ax + b = c. Addition and Subtraction Properties of equality: Let a, b, and c represent algebraic expression. 1. Addition property of equality: If a = b, then a + c = b + c 2. Subtraction property of equality: If a = b, then a – c = b – c 3. Multiplication property of equality: If a = b, then ac = bc (where c not equal to 0) 4. Division property of equality: If a = b, then a/c = b/c (where c not equal to 0) Examples: 1. Solve: x – 2 = 10 x – 2 + 2 = 10 + 2 We want to get x by itself. In order do this, we have to move -­‐2. X = 12 2. Solve: 13 + b = -­‐13 13 – 13 + b = -­‐13 – 13 Subtract 13 from both side to isolate the variable. b = -­‐ 26 3. Solve: 6 = = -­‐ 2x 6(-­‐1/2) = -­‐2(-­‐1/2)x Multiply both sides by the reciprocal -­‐1/2 to isolate the variable. -­‐3 = x 4. Solve: -­‐2/5x = 10 (-­‐2/5)(-­‐5/2)x = 10(-­‐5/2) Multiply both sides by -­‐5/2 to isolate the variable x = -­‐25 5. Write an algebraic equation to represent each English sentence. Then solve the equation. a. The sum of thirty-­‐one and a number is thirteen. 31 + x = 13 31 – 31 + x = 13 – 31 x = -­‐18 b. The product of negative three and a number is the same as twenty-­‐four. -­‐3x = 24 -­‐3(-­‐1/3)x = 24(-­‐1/3) x = -­‐8 c. The value of -­‐3 subtracted from a number is 4. x – (-­‐3) = 4 x + 3 = 4 x + 3 – 3 = 4 – 3 x = 1